Systems, methods and apparatuses for guidance and alignment in electric vehicles wireless inductive charging systems

ABSTRACT

An apparatus for determining a relative position of a wireless power transmitter from a wireless power receiver is provided. The apparatus comprises a plurality of sense coils, each configured to generate a respective signal under influence of an alternating magnetic field comprising a plurality of wave pulses, each wave pulse occurring in a respective time slot of a plurality of time slots. The apparatus further comprises a processor configured to determine the relative position of the wireless power transmitter from the wireless power receiver based on the respective signal from each of the plurality of sense coils.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.15/069,570 entitled “SYSTEMS, METHODS AND APPARATUSES FOR GUIDANCE ANDALIGNMENT IN ELECTRIC VEHICLES WIRELESS INDUCTIVE CHARGING SYSTEMS”filed Mar. 14, 2016, which claims priority to and the benefit under 35U.S.C. § 119(e) of U.S. Provisional Patent Application No. 62/183,661entitled “SYSTEMS, METHODS AND APPARATUSES FOR GUIDANCE AND ALIGNMENT INELECTRIC VEHICLES WIRELESS INDUCTIVE CHARGING SYSTEMS” filed on Jun. 23,2015, the disclosures of which are hereby incorporated by reference intheir entireties.

FIELD

This application is generally related to wireless charging powertransfer applications, and specifically to systems, methods andapparatuses for guidance and alignment of electric vehicles withwireless inductive charging power transmitters. More specifically thepresent disclosure relates to determining a position of the electricvehicle relative to a ground-based charging unit based on magneticvector fields (magnetic vectoring) and receiver synchronization methodsfor magnetic vectoring.

BACKGROUND

Efficiency in wireless inductive charging power applications depends atleast in part on achieving at least a minimum alignment thresholdbetween a wireless power transmitter and a wireless power receiver. Onemethod for aiding such alignment is the use of magnetic vectoring, wherea distance and/or direction between the wireless power transmitter andthe wireless power receiver is determined based on sensing one or moreattributes of a magnetic field generated at or near either the wirelesspower transmitter or the wireless power receiver (the magnetic field maynot be for wireless power transfer but for guidance and alignmentpurposes). However, determining a non-ambiguous position between awireless power transmitter and a wireless power receiver utilizingmagnetic vectoring requires some form of synchronization of the magneticfield detection system with the magnetic field generating system.Accordingly, systems, methods and apparatuses for guidance and alignmentof electric vehicles with wireless inductive charging power transmittersas described herein are desirable.

SUMMARY

In some implementations, an apparatus for determining a relativeposition of a wireless power transmitter from a wireless power receiveris provided. The apparatus comprises a plurality of sense coils, eachconfigured to generate a respective signal under influence of analternating magnetic field comprising a plurality of wave pulses, eachwave pulse occurring in a respective time slot of a plurality of timeslots. The apparatus further comprises a processor configured todetermine the relative position of the wireless power transmitter fromthe wireless power receiver based on the respective signal from each ofthe plurality of sense coils.

In some other implementations, a method for determining a relativeposition of a wireless power transmitter from a wireless power receiveris provided. The method comprises generating, by each of a plurality ofsense coils, a respective voltage signal under influence of analternating magnetic field comprising a plurality of wave pulses, eachwave pulse occurring in a respective time slot of a plurality of timeslots. The method comprises determining the relative position of thewireless power transmitter from the wireless power receiver based on therespective voltage signal from each of the plurality of sense coils.

In some other implementations, a non-transitory, computer-readablemedium comprises code that, when executed, causes an apparatus fordetermining a relative position of a wireless power transmitter from awireless power receiver to generate, by each of a plurality of sensecoils, a respective voltage signal under influence of an alternatingmagnetic field comprising a plurality of wave pulses, each wave pulseoccurring in a respective time slot of a plurality of time slots. Thecode, when executed further causes the apparatus to determine therelative position of the wireless power transmitter from the wirelesspower receiver based on the respective voltage signal from each of theplurality of sense coils.

In some other implementations, an apparatus for determining a relativeposition of a wireless power transmitter from a wireless power receiveris provided. The apparatus comprises a plurality of means for generatinga respective voltage signal under influence of an alternating magneticfield comprising a plurality of wave pulses, each wave pulse occurringin a respective time slot of a plurality of time slots. The apparatusfurther comprises means for determining the relative position of thewireless power transmitter from the wireless power receiver based on therespective voltage signal from each of the plurality of means forgenerating the respective voltage signal.

In some other implementations, an apparatus for determining a relativeposition of a wireless power transmitter from a wireless power receiveris provided. The apparatus comprises a driver circuit configured togenerate at least a first signal, a second signal and a third signal,each comprising at least one respective wave pulse of a plurality ofwave pulses, each wave pulse occurring in a respective time slot of aplurality of time slots. The apparatus comprises a plurality of coilsconfigured to generate an alternating magnetic field while being drivenby a respective one of the first signal, the second signal and the thirdsignal.

In some other implementations, a method for determining a relativeposition of a wireless power transmitter from a wireless power receiveris provided. The method comprises generating at least a first signal, asecond signal and a third signal, each comprising at least onerespective wave pulse of a plurality of wave pulses, each wave pulseoccurring in a respective time slot of a plurality of time slots. Themethod comprises generating an alternating magnetic field by drivingeach coil of a plurality of coils with a respective one of the firstsignal, the second signal and the third signal.

In some other implementations, a non-transitory, computer-readablemedium comprises code that, when executed, causes an apparatus fordetermining a relative position of a wireless power transmitter from awireless power receiver to generate at least a first signal, a secondsignal and a third signal, each comprising at least one respective wavepulse of a plurality of wave pulses, each wave pulse occurring in arespective time slot of a plurality of time slots. The code whenexecuted further causes the apparatus to generate an alternatingmagnetic field by driving each coil of a plurality of coils with arespective one of the first signal, the second signal and the thirdsignal.

In some other implementations, an apparatus for determining a relativeposition of a wireless power transmitter from a wireless power receiveris provided. The apparatus comprises means for generating at least afirst signal, a second signal and a third signal, each comprising atleast one respective wave pulse of a plurality of wave pulses, each wavepulse occurring in a respective time slot of a plurality of time slots.The apparatus comprises a plurality of means for generating analternating magnetic field by being driven with a respective one of thefirst signal, the second signal and the third signal.

In some other implementations, an apparatus for determining a relativeposition of a wireless power transmitter from a wireless power receiveris provided. The apparatus comprises a plurality of sense coils, eachconfigured to generate a respective voltage signal under influence of analternating magnetic field comprising a plurality of beacon signalsoccurring simultaneously, each beacon signal modulated with a uniquespreading code. The apparatus further comprises a processor configuredto determine the relative position of the wireless power transmitterfrom the wireless power receiver based on the respective voltage signalfrom each of the plurality of sense coils.

In some other implementations, a method for determining a relativeposition of a wireless power transmitter from a wireless power receiveris provided. The method comprises generating, by each of a plurality ofsense coils, a respective voltage signal under influence of analternating magnetic field comprising a plurality of beacon signalsoccurring simultaneously, each beacon signal modulated with a uniquespreading code. The method comprises determining the relative positionof the wireless power transmitter from the wireless power receiver basedon the respective voltage signal from each of the plurality of sensecoils.

In some other implementations, a non-transitory, computer-readablemedium comprises code that, when executed, causes an apparatus fordetermining a relative position of a wireless power transmitter from awireless power receiver to generating, by each of a plurality of sensecoils, a respective voltage signal under influence of an alternatingmagnetic field comprising a plurality of beacon signals occurringsimultaneously, each beacon signal modulated with a unique spreadingcode. The method comprises determining the relative position of thewireless power transmitter from the wireless power receiver based on therespective voltage signal from each of the plurality of sense coils.

In some other implementations, an apparatus for determining a relativeposition of a wireless power transmitter from a wireless power receiveris provided. The apparatus comprises a plurality of means for generatinga respective voltage signal under influence of an alternating magneticfield comprising a plurality of beacon signals occurring simultaneously,each beacon signal modulated with a unique spreading code. The apparatusfurther comprises means for determining the relative position of thewireless power transmitter from the wireless power receiver based on therespective voltage signal from each of the plurality of sense coils.

In some other implementations, an apparatus for determining a relativeposition of a wireless power transmitter from a wireless power receiveris provided. The apparatus comprises a driver circuit configured togenerate at least a first signal, a second signal and a third signal,each comprising a respective beacon signal of a plurality of beaconsignals occurring simultaneously, each beacon signal modulated with aunique spreading code. The apparatus comprises a plurality of coilsconfigured to generate an alternating magnetic field while being drivenby a respective one of the first signal, the second signal and the thirdsignal.

In some other implementations, a method for determining a relativeposition of a wireless power transmitter from a wireless power receiveris provided. The method comprises generating at least a first signal, asecond signal and a third signal, each comprising a respective beaconsignal of a plurality of beacon signals occurring simultaneously, eachbeacon signal modulated with a unique spreading code. The methodcomprises generating an alternating magnetic field by driving each coilof a plurality of coils with a respective one of the first signal, thesecond signal and the third signal.

In some other implementations, a non-transitory, computer-readablemedium comprises code that, when executed, causes an apparatus fordetermining a relative position of a wireless power transmitter from awireless power receiver to generate at least a first signal, a secondsignal and a third signal, each comprising a respective beacon signal ofa plurality of beacon signals occurring simultaneously, each beaconsignal modulated with a unique spreading code. The code when executedfurther causes the apparatus to generate an alternating magnetic fieldby driving each coil of a plurality of coils with a respective one ofthe first signal, the second signal and the third signal.

In some other implementations, an apparatus for determining a relativeposition of a wireless power transmitter from a wireless power receiveris provided. The apparatus comprises means for generating at least afirst signal, a second signal and a third signal, each comprising arespective beacon signal of a plurality of beacon signals occurringsimultaneously, each beacon signal modulated with a unique spreadingcode. The apparatus comprises a plurality of means for generating analternating magnetic field by being driven with a respective one of thefirst signal, the second signal and the third signal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a functional block diagram of a wireless power transfersystem, in accordance with some implementations.

FIG. 2 is a functional block diagram of a wireless power transfersystem, in accordance with some other implementations.

FIG. 3 is a schematic diagram of a portion of transmit circuitry orreceive circuitry of FIG. 2 including a transmit or receive coupler, inaccordance with some implementations.

FIG. 4A illustrates a positional relationship between a vehicle-basedmagnetic field sensor and a ground-based magnetic field generatorinstalled in a parking stall, the sensor's position and rotationrepresented in the generator's coordinate frame.

FIG. 4B illustrates a positional relationship between a vehicle-basedmagnetic field sensor and a ground-based magnetic field generatorinstalled in a parking stall, the generator's position and rotationrepresented in the sensor's coordinate frame.

FIG. 4C illustrates a positional relationship between a vehicle-basedmagnetic field generator and a ground-based magnetic field sensorinstalled in a parking stall, the generator's position and rotationrepresented in the sensor's coordinate frame.

FIG. 4D illustrates a positional relationship between of a vehicle-basedmagnetic field generator and a ground-based magnetic field sensorinstalled in a parking stall, the sensor's position and rotationrepresented in the generator's coordinate frame.

FIG. 5 is an illustration of a vehicle in a parking lot includingstructures and parking lot markings that can be used for positioning andaligning the vehicle.

FIG. 6 illustrates a 3-axis magnetic field generator and a 3-axismagnetic field sensor based on an orthogonal arrangement of wire loops,in accordance with some implementations.

FIG. 7A illustrates a plurality of frequencies for use infrequency-division magnetic field multiplexing, in accordance with someimplementations.

FIG. 7B illustrates a plurality of time slots for use in time-divisionmagnetic field multiplexing, in accordance with some implementations.

FIG. 7C illustrates a plurality of time slots for use in time-divisionmagnetic field multiplexing, in accordance with some otherimplementations.

FIG. 8 illustrates a block diagram of a magnetic field position-findingsystem, in accordance with some implementations.

FIG. 9 illustrates magnetic moments of a magnetic field generated by a3-axis generator and the resulting magnetic field vector triples at eachof six different on-axis positions, in accordance with someimplementations.

FIG. 10A illustrates a magnetic radio compass using an x-y-oscilloscope,in accordance with some implementations.

FIG. 10B illustrates a magnetic radio compass obtaining absolute phaseinformation from a reference signal, in accordance with someimplementations.

FIG. 11A shows a non-sinusoidal transmission signal suitable forresolving polarity ambiguity, in accordance with some implementations.

FIG. 11B shows an amplitude-modulated reference signal suitable forproviding a receiver with synchronization information, in accordancewith some implementations.

FIG. 12 illustrates a magnetic radio compass displaying orientations oftwo magnetic field vectors, in accordance with some implementations.

FIG. 13 shows the different combinations of magnetic vector polaritythat may be resolved with supplementary synchronization information, inaccordance with some implementations.

FIG. 14 displays field lines of a magnetic field generated by a 2-axismagnetic field generator and magnetic vector pairs present at 4 on-axispositions and 4 off-axis positions, in accordance with someimplementations.

FIG. 15 illustrates vector polarity ambiguity in a system using a 2-axisgenerator and only relative phase synchronization, in accordance withsome implementations.

FIGS. 16A and 16B show vehicle parking scenarios that illustrateposition and rotation ambiguity in a system using a 2-axis generator andonly relative phase synchronization, in accordance with someimplementations.

FIG. 17 displays a phase difference Δφ of a double-tone signal as afunction of time, in accordance with some implementations.

FIG. 18 illustrates a block diagram of a synchronous detector of amagnetic field positioning receiver, in accordance with someimplementations.

FIG. 19 shows a block diagram of a portion of a magnetic fieldpositioning receiver using a bank of the synchronous detectors of FIG.18, in accordance with some implementations.

FIGS. 20A, 20B and 20C illustrate complex phasors at different stages ofreceiver synchronization and for different outputs of a sub-bank ofsynchronous detector, in accordance with some implementations.

FIG. 21 illustrates a block diagram of an analog front end (AFE) of a3-axis magnetic field positioning receiver, in accordance with someimplementations.

FIG. 22 illustrates an orthogonal coil arrangement for a 3-axisgenerator or sensor, in accordance with some implementations.

FIG. 23 illustrates a frequency division 4-tone magnetic fieldtransmission scheme, in accordance with some implementations.

FIG. 24 illustrates a modulation waveform of a transmission framecomprising a synchronization sequence and a multi-tone transmission, inaccordance with some implementations.

FIG. 25 shows a sequence of modulated single-carrier wave pulsestransmitted during different time slots, in accordance with someimplementations.

FIG. 26 shows the sequence of the wave pulses of FIG. 25 as receivedduring the different time slots as altered by the transmission channel,in accordance with some implementations.

FIG. 27 shows a block diagram of a synchronous detector of a magneticfield positioning receiver operating in time-division mode in accordancewith some implementations.

FIG. 28 shows a block diagram of a portion of a 3-branch magnetic fieldpositioning receiver operating in time-division mode using a synchronousdetector per sensed magnetic field component, in accordance with someimplementations.

FIGS. 29A and 29B show complex phasors as sequentially detected by thex-branch synchronous detector in consecutive time slots before and afterphasor rotation, respectively, in accordance with some implementations.

FIG. 30 shows a block diagram of a correlation detector of a magneticfield positioning receiver operating in code-division mode, inaccordance with some implementations.

FIG. 31 shows a block diagram of a portion of a 3-branch magnetic fieldpositioning receiver operating in code-division mode using a correlationdetector per magnetic field beacon signal and per sensed magnetic fieldcomponent, in accordance with some implementations.

FIGS. 32A and 32B show complex phasors as simultaneously detected by thex-branch synchronous detector before and after phasor rotation,respectively, in accordance with some implementations.

FIG. 33 is a flowchart depicting a method for determining a positionbetween a wireless power transmitter and a wireless power receiver, inaccordance with some implementations.

FIG. 34 is a flowchart depicting a method for determining a relativeposition of a wireless power transmitter from a wireless power receiver,in accordance with some implementations.

FIG. 35 is a flowchart depicting a method for determining a positionbetween a wireless power transmitter and a wireless power receiver, inaccordance with some implementations.

FIG. 36 is a flowchart depicting a method for determining a relativeposition of a wireless power transmitter from a wireless power receiver,in accordance with some implementations.

DETAILED DESCRIPTION

In the following detailed description, reference is made to theaccompanying drawings, which form a part of the present disclosure. Theillustrative implementations described in the detailed description,drawings, and claims are not meant to be limiting. Other implementationsmay be utilized, and other changes may be made, without departing fromthe spirit or scope of the subject matter presented here. It will bereadily understood that the aspects of the present disclosure, asgenerally described herein, and illustrated in the Figures, can bearranged, substituted, combined, and designed in a wide variety ofdifferent configurations, all of which are explicitly contemplated andform part of this disclosure.

Wireless power transfer may refer to transferring any form of energyassociated with electric fields, magnetic fields, electromagneticfields, or otherwise from a transmitter to a receiver without the use ofphysical electrical conductors (e.g., power may be transferred throughfree space). The power output into a wireless field (e.g., a magneticfield or an electromagnetic field) may be received, captured, or coupledby a “receive coupler” to achieve power transfer.

The terminology used herein is for the purpose of describing particularimplementations only and is not intended to be limiting on thedisclosure. It will be understood that if a specific number of a claimelement is intended, such intent will be explicitly recited in theclaim, and in the absence of such recitation, no such intent is present.For example, as used herein, the singular forms “a,” “an” and “the” areintended to include the plural forms as well, unless the context clearlyindicates otherwise. As used herein, the term “and/or” includes any andall combinations of one or more of the associated listed items. It willbe further understood that the terms “comprises,” “comprising,”“includes,” and “including,” when used in this specification, specifythe presence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof. Expressions such as “at least oneof,” when preceding a list of elements, modify the entire list ofelements and do not modify the individual elements of the list.

FIG. 1 is a functional block diagram of a wireless power transfer system100, in accordance with some implementations. Input power 102 may beprovided to a transmitter 104 from a power source (not shown) togenerate a wireless (e.g., magnetic or electromagnetic) field 105 via atransmit coupler 114 for performing energy transfer. The receiver 108may receive power when the receiver 108 is located in the wireless field105 produced by the transmitter 104. The wireless field 105 correspondsto a region where energy output by the transmitter 104 may be capturedby the receiver 108. A receiver 108 may couple to the wireless field 105and generate output power 110 for storing or consumption by a device(not shown in this figure) coupled to the output power 110. Both thetransmitter 104 and the receiver 108 are separated by a distance 112.

In one example implementation, power is transferred inductively via atime-varying magnetic field generated by the transmit coupler 114. Thetransmitter 104 and the receiver 108 may further be configured accordingto a mutual resonant relationship. When the resonant frequency of thereceiver 108 and the resonant frequency of the transmitter 104 aresubstantially the same or very close, transmission losses between thetransmitter 104 and the receiver 108 are minimal. However, even whenresonance between the transmitter 104 and receiver 108 are not matched,energy may be transferred, although the efficiency may be reduced. Forexample, the efficiency may be less when resonance is not matched.Transfer of energy occurs by coupling energy from the wireless field 105of the transmit coupler 114 to the receive coupler 118, residing in thevicinity of the wireless field 105, rather than propagating the energyfrom the transmit coupler 114 into free space. Resonant inductivecoupling techniques may thus allow for improved efficiency and powertransfer over various distances and with a variety of inductive couplerconfigurations.

In some implementations, the wireless field 105 corresponds to the“near-field” of the transmitter 104. The near-field may correspond to aregion in which there are strong reactive fields resulting from thecurrents and charges in the transmit coupler 114 that minimally radiatepower away from the transmit coupler 114. The near-field may correspondto a region that is within about one wavelength (or a fraction thereof)of the transmit coupler 114. Efficient energy transfer may occur bycoupling a large portion of the energy in the wireless field 105 to thereceive coupler 118 rather than propagating most of the energy in anelectromagnetic wave to the far field. When positioned within thewireless field 105, a “coupling mode” may be developed between thetransmit coupler 114 and the receive coupler 118.

FIG. 2 is a functional block diagram of a wireless power transfer system200, in accordance with some other implementations. The system 200 maybe a wireless power transfer system of similar operation andfunctionality as the system 100 of FIG. 1. However, the system 200provides additional details regarding the components of the wirelesspower transfer system 200 as compared to FIG. 1. The system 200 includesa transmitter 204 and a receiver 208. The transmitter 204 includestransmit circuitry 206 that includes an oscillator 222, a driver circuit224, and a filter and matching circuit 226. The oscillator 222 may beconfigured to generate a signal at a desired frequency that may beadjusted in response to a frequency control signal 223. The oscillator222 provides the oscillator signal to the driver circuit 224. The drivercircuit 224 may be configured to drive the transmit coupler 214 at aresonant frequency of the transmit coupler 214 based on an input voltagesignal (V_(D)) 225.

The filter and matching circuit 226 filters out harmonics or otherunwanted frequencies and matches the impedance of the transmit circuitry206 to the transmit coupler 214. As a result of driving the transmitcoupler 214, the transmit coupler 214 generates a wireless field 205 towirelessly output power at a level sufficient for charging a battery236.

The receiver 208 comprises receive circuitry 210 that includes amatching circuit 232 and a rectifier circuit 234. The matching circuit232 may match the impedance of the receive circuitry 210 to theimpedance of the receive coupler 218. The rectifier circuit 234 maygenerate a direct current (DC) power output from an alternate current(AC) power input to charge the battery 236. The receiver 208 and thetransmitter 204 may additionally communicate on a separate communicationchannel 219 (e.g., Bluetooth, Zigbee, cellular, etc.). The receiver 208and the transmitter 204 may alternatively communicate via in-bandsignaling using characteristics of the wireless field 205. In someimplementations, the receiver 208 may be configured to determine whetheran amount of power transmitted by the transmitter 204 and received bythe receiver 208 is appropriate for charging the battery 236.

FIG. 3 is a schematic diagram of a portion of the transmit circuitry 206or the receive circuitry 210 of FIG. 2, in accordance with someimplementations. As illustrated in FIG. 3, transmit or receive circuitry350 may include a coupler 352. The coupler 352 may also be referred toor be configured as a “conductor loop”, a coil, an inductor, or a“magnetic” coupler. The term “coupler” generally refers to a componentthat may wirelessly output or receive energy for coupling to another“coupler.”

The resonant frequency of the loop or magnetic couplers is based on theinductance and capacitance of the loop or magnetic coupler. Inductancemay be simply the inductance created by the coupler 352, whereas,capacitance may be added via a capacitor (or the self-capacitance of thecoupler 352) to create a resonant structure at a desired resonantfrequency, or at a fixed frequency set or prescribed by a particularoperations standard. As a non-limiting example, a capacitor 354 and acapacitor 356 may be added to the transmit or receive circuitry 350 tocreate a resonant circuit that selects a signal 358 at a resonantfrequency. For larger sized couplers using large diameter couplersexhibiting larger inductance, the value of capacitance needed to produceresonance may be lower. Furthermore, as the size of the couplerincreases, coupling efficiency may increase. This is mainly true if thesize of both transmit and receive couplers increase. For transmitcouplers, the signal 358, oscillating at a frequency that substantiallycorresponds to the resonant frequency of the coupler 352, may be aninput to the coupler 352. In some implementations, the frequency forinductive power transfer may be in the range of 20 kHz to 150 kHz.

In order to maintain a requisite threshold of efficiency and compliancewith regulatory standards, inductive charging of electric vehicles inthe kilowatt range require relatively tight coupling; the higher thepower transfer, the tighter the coupling requirement to maintain EMIlevels within compliance of regulatory standards. For example, inductivepower transfer (IPT) of 3 kW from a ground-based charging unit to avehicle-based charging unit over an air gap typically in the range of70-150 mm may tolerate alignment errors of up to approximately 150 mm,depending on the technology and design of the couplers used. For systemsinductively transferring energy at 20 kW, the tolerable alignment errormay be less than 50 mm, requiring considerably higher parking precision.

Parking assist systems can potentially help to overcome such alignmentissues, thereby increasing convenience and user experience. This isparticularly true for position-critical electric vehicle charging. Asystem that assists a driver in reliably parking an electric vehiclewithin a so-called “sweet spot” of the coupler system may generally becalled a guidance and alignment system. The “sweet spot” may define azone of alignments between the vehicle-based IPT coupler and aground-based IPT coupler where coupling efficiency is above a certainminimum value. Such a “sweet spot” may also be defined in terms ofemissions, e.g., if the electric vehicle is parked in this “sweet spot,”the leakage of the magnetic field, as measured in the area surroundingthe vehicle may be below regulatory limits, e.g., ICNIRP limits forelectro-motive force (EMF) or electro-magnetic interference (EMI)exposure.

In a minimum solution, the system may simply indicate whether thevehicle has been parked within such a “sweet spot” or not. This mayalways be needed even in case of an IPT technology that is very tolerantto alignment errors.

A more sophisticated system, which is the subject of this application,determines a position of a vehicle reference point relative to a basereference point. This position data may be translated into visual and/oracoustic guidance and alignment information to assist the driver of theelectric vehicle in reliably parking the vehicle within the “sweet spot”of the charging system so as to avoid failed alignment attempts. Thedriver may use this feedback to correct the trajectory towards thecharging spot in real-time and to stop the vehicle within the “sweetspot.” Such guidance information may be particularly useful for IPTsystems having small alignment tolerances or in conditions that renderparking for charging difficult (e.g., by night or snow clad parkinglots). In an advanced and yet more sophisticated system, positioninformation may be used to park a vehicle automatically with no or onlyminimal driver intervention (drive by wire).

Both “guidance” and “alignment” of such an electric vehicle may rely ona local positioning system having components aboard the electric vehicleand components installed in a parking lot (e.g., infrastructure).Systems, devices and methods disclosed herein for positioning are basedon generating and sensing a low frequency magnetic field that may begenerated either by the base charging unit or by the vehicle chargingunit at a frequency preferably below 150 kHz. Such methods, disclosedherein, are referred to as magnetic vectoring and may be used forpositioning at a distance range of between 0 and 5 meters from thesource of the low frequency magnetic field.

Alignment and particularly guidance may be based at least on determiningan accurate position of the vehicle relative to the charging base. Theremay be several technical approaches to such positioning or localization.These approaches may be based on optical or infrared methods usingcameras, appropriate road markings and/or laser scanners, inertialsystems using accelerometers and/or gyrometers, measuring propagationtime and performing triangulation of acoustic (ultrasonic) waves orelectromagnetic waves (e.g., microwaves), and/or sensing a magneticnear-field that may be generated by the base charging unit, vehiclecharging unit or by other external devices.

A positioning/localization method should be reliably functional insubstantially all conditions as experienced in an automotive environmentindoors (no GPS reception) and outdoors, in different seasonal weatherconditions (snow, ice, water, foliage), at different day times (sunirradiation, darkness), with signal sources and sensors polluted (dirt,mud, dust, etc.), with different ground properties (asphalt,ferroconcrete), and/or in the presence of vehicles and other reflectingor line-of-sight obstructing objects (e.g., wheels of own vehicle,vehicles parked adjacent, etc.). Moreover, for the sake of minimizinginfrastructure installation complexity and costs, methods allowing fullintegration of all system components into the base charging unit and/orvehicle charging unit and not requiring installation of additionalcomponents external to these units (e.g., signal sources, antennas,etc.) are desirable. Considering all of above aspects, sensing amagnetic near field has been found particularly promising for alignmentand guidance within a parking stall and in the surrounding area.

A basic method of sensing the magnetic field for purposes of positioningassumes that at least one of a charging base or vehicle generates analternating magnetic field that can be sensed by a sensor system, whichmay be either integrated into the vehicle charging unit or built intothe charging base, respectively. In some implementations, the frequencyof the sensing magnetic field may be substantially the same as theoperating frequency of the IPT system. In some other implementations,the frequency of the sensing magnetic field may be different from theIPT frequency, but low enough so that sensing (e.g., positioning) takesplace in the so-called near-field (e.g., within ½π or ˜15.9% of awavelength) of the sensing magnetic field. A suitable frequency may bein a low frequency (LF) band (e.g., in the range from 120-140 kHz),however, a frequency in a high frequency (HF) band (e.g., in the 6.78MHz or 13.56 MHz ISM-band) may also be utilized. In addition, in someimplementations, the sense magnetic field may be generated using thesame coil or the same coil arrangement that is used for IPT (e.g., thetransmit coupler 274 of FIG. 2 or the transmit coupler 352 of FIG. 3).However for higher accuracy and wider applicability, use of one or moreseparate coils specifically for the purpose of positioning may beadvantageous.

In some implementations presenting a simple, low cost solution, only analignment score representative of the coupling strength between one ormore coil generating the sense magnetic field and one or more sensecoils receiving the generated sense magnetic field is determined but thesystem may not be able to provide a driver of the electric vehicle withany more information (e.g., actual alignment error and/or how the drivershould correct in case of a failed alignment attempt). In such lowcomplexity solutions, the sense magnetic field may be generated by theone or more primary IPT coils of the base unit and an alignment score isdetermined by measuring, e.g., the vehicle's secondary coil shortcircuit current or open circuit voltage using current/voltagetransducers that may also be used for controlling and monitoring the IPTsystem. In such low complexity solutions, primary current of the one ormore primary coils required in the alignment mode may be lower thanduring regular IPT operation. However, the magnetic and/or electricfields generated may still be too high to meet applicable regulatorylimits, e.g., a human exposure standard or an OEM-specified limit. Thismay be particularly true if the alignment mode is activated before thevehicle has fully parked over the one or more primary coils of thecharging base.

In some other, more sophisticated implementations, magnetic fieldsensing may provide position information over an extended range that canbe used to assist the driver in accurately parking the vehicle withinthe “sweet” spot. Such systems may require dedicated active fieldsensors that are frequency selective and considerably more sensitivethan ordinary current or voltage transducers used for wirelesslytransferring power. Furthermore, such a system has the potential tooperate at lower magnetic and electric field levels that are compliantwith human exposure standards in all situations.

Yet other even more sophisticated implementations may provide higherpositioning accuracy and wider applicability by utilizing one or morededicated coils for generating the magnetic field. These generator coilsmay be arranged and configured for generating a more complex magneticfield pattern that may be utilized to resolve position ambiguity issues,as will be described in more detail below. Sensing the magnetic nearfield may also apply for positioning outside a parking stall in anextended area, e.g., inside a parking garage. In such implementations,magnetic field sources may be road-embedded, e.g., in the access aisles.Such designs may also be used for dynamic roadway powering and chargingsystems.

One difficulty of quasi-static magnetic field (near field) positioningtechniques based on sensing an alternating (sinusoidal) magnetic fieldis the requirement for synchronization between magnetic field generatorand magnetic field sensor. Absence of any synchronization informationleads to a signal polarity (180° phase) ambiguity issue and consequentlyto position ambiguity. The 180° phase ambiguity is a problem of themagnetic radio compass, which has been used for radio direction finding,e.g., in nautical and aeronautical navigation systems. It is also aproblem in magnetic field-based vehicle positioning systems used forguidance and alignment of an electric vehicle for purposes of inductivecharging.

The present application mainly relates to the magnetic vector polarityissue and to methods and systems for achieving the necessarysynchronization between magnetic field transmitter and receiver inpositioning systems using a multi-axis magnetic field generator and amulti-axis magnetic field sensor. Some implementations herein assume amulti-tone scheme (FDM) to transmit magnetic beacon signals in differentaxes. The rational behind FDM is low complexity, spectral efficiency,robustness against interference and high dynamic range as needed to copewith the “near-far” effects as typically encountered in magnetic nearfield transmissions.

The 3-axis or 2-axis generator/3-axis sensor position finding problem ofvehicle charging only requires knowledge of the relative signal (vector)polarities and thus relative phase synchronization between tones of anFDM transmission. As opposed to absolute phase, relative phasesynchronization can be achieved in-band by either using a narrow-bandmodulated signal or in a very simple way by using a double-tonetransmission in at least one of the generator axis.

Preferably, this double-tone has a tone separation equal to thefrequency separation of tones transmitted in other axis resulting in aFDM transmission scheme with equal spacing between adjacent tonefrequencies. In the receiver, these tones and tones emanating from otherpositioning transmitters may be separated using Fast Fourier TransformTechniques with high side-lobe and thus high cross-talk and adjacentchannel attenuation.

FIGS. 4A, 4B, 4C, 4D illustrate different positional relationshipsbetween a charging base (e.g., a base pad) 402 and a vehicle chargingunit, e.g., a vehicle pad) 404 using one of a ground-based coordinateframe and a vehicle-based coordinate frame. FIGS. 4A, 4B, 4C, 4D assumea magnetic vectoring (MV) field generator and a MV field sensor areintegrated with the IPT couplers in the base pad 402 and the vehicle pad404 of a vehicle 406 in positions such that the magnetic centers of therespective IPT coupler and of the MV generator coincide. Furthermore,FIGS. 4A, 4B, 4C, 4D assume any magnetic field polarization axis of thebase IPT coupler and of the vehicle IPT coupler are equally orientedwith any of the axes of the MV field generator and MV field sensor,respectively, such that a single coordinate frame from the perspectiveof each of the MV field generator and the MV field sensor is required todefine a positional relationship between a base IPT coupler and avehicle IPT coupler. Moreover, FIGS. 4A, 4B, 4C, 4D assume that the axisof the ground-based coordinate frame is oriented parallel to the parkingstall outline as indicated in FIGS. 4A-4D by a parking stall marking,and that the vehicle-based coordinate frame axis is oriented parallel tothe vehicle's symmetry axis.

The above assumptions have been made for the sake of simplicity andclarity and should not be construed as either a requirement orprecluding other configurations and arrangements. For example, thecoordinate frames of the IPT couplers may differ from the coordinateframes of the MV generator and sensor in position and orientation. Thecoordinate frames may also differ from any symmetry axis as defined bythe parking stall and/or the vehicle geometry. In such implementations,additional positional relationships among the different coordinateframes should be defined.

For FIGS. 4A, 4B, 4C, 4D, the magnetic centers of the IPT couplers maybe defined as a first point in the base IPT coupler (e.g., the transmitcoupler 214 of FIG. 2) and a second point in the vehicle IPT coupler(e.g., the receive coupler 218 of FIG. 2) where the first point and thesecond point have essentially zero horizontal (e.g., x or y axis) offsetfrom one another when IPT coupling is at a maximum for any amount ofrotation of the vehicle 406 that is within constraints dictated by thetype of IPT coupler. For “polarized” IPT couplers, this definition formagnetic centers of the IPT couplers may hold for rotations of thevehicle restricted to within approximately ±30° and/or 150°-210°.Normally, the magnetic center of a particular IPT coupler is locatedapproximately on a symmetry axis of the magnetic field generated by thatparticular IPT coupler.

Likewise, the magnetic centers of the MV field generator and of the MVfield sensor may be defined as a first point in the generator and asecond point in the sensor where the first point and the second pointhave essentially zero horizontal offset from one another when thepositioning system determines that an essentially zero relativehorizontal offset between the first point and the second point has beenreached for any azimuthal rotation of the sensor.

As shown in FIGS. 4A, 4B, 4C, 4D, the x-axis and y-axis always refer tothe coordinate frame from the perspective of the MV field sensor, whilethe x′-axis and y′-axis always refer to the coordinate frame from theperspective of the MV field generator. This is true regardless ofwhether the MV field sensor is located in the base pad (see FIGS. 4C and4D) or in the vehicle pad (see FIGS. 4A and 4B). The z-axis and thez′-axis, respectively, are not shown in FIGS. 4A, 4B, 4C, 4D but areassumed to point towards the sky (e.g., the zenith), thus defining a“right-handed” or “positive” coordinate system. These coordinate systemswill be referenced throughout this application.

FIGS. 4A, 4B illustrate a positional relationship between a ground-basedgenerator and a vehicle-mounted sensor, in accordance with someimplementations. In FIG. 4A, position and rotation of the sensor arerepresented in generator coordinates by a position vector r′={rightarrow over (O′P′)} where O′ and P′ denote the magnetic center points ofthe generator and sensor, respectively, and where P′ is represented inthe generator's coordinate frame, having its origin at O′. The rotationof the sensor's coordinate frame with respect to the generator'scoordinate frame (e.g., an angle of intersection between the x-axis ofthe sensor's coordinate frame and the x′-axis of the generator'scoordinate frame) is defined by the angle of rotation ψ′ measured fromthe x′-axis. Using polar coordinates, the sensor's position and rotationmay be defined by azimuth angle α′ measured from the x′-axis, thedistance ρ′ (length of r′), and ψ′, respectively, as defined withrespect to the generator's coordinate frame.

In FIG. 4B, position and rotation of the generator are represented insensor coordinates by a position vector r={right arrow over (OP)} whereO and P denote the magnetic center points of sensor and the generator,respectively, and where P is represented in the sensor's coordinateframe, having its origin at O. The rotation of the generator'scoordinate frame with respect to the sensor's coordinate frame (e.g., anangle of intersection between the x′-axis of the generator's coordinateframe and the x-axis of the sensor's coordinate frame) is defined by theangle of rotation ψ measured from the x-axis. Using polar coordinates,the generator's position and rotation may be defined by azimuth angle αmeasured from the x-axis, the distance ρ (length of r), and ψ,respectively, as defined with respect to the sensor's coordinate frame.

FIGS. 4C and 4D illustrate a positional relationship between avehicle-mounted generator and ground-based sensor, in accordance withsome implementations. In FIG. 4C, position and rotation of the generatorare represented in sensor coordinates by a position vector r={rightarrow over (OP)} where O and P denote the magnetic center points ofsensor and the generator, respectively, and where P is represented inthe sensor's coordinate frame, having its origin at O. The rotation ofthe generator's coordinate frame with respect to the sensor's coordinateframe (e.g., an angle of intersection between the x′-axis of thegenerator's coordinate frame and the x-axis of the sensor's coordinateframe) is defined by the angle of rotation ψ measured from the x-axis.Using polar coordinates, the generator's position and rotation may bedefined by azimuth angle α measured from the x-axis, the distance ρ(length of r), and ψ, respectively, as defined with respect to thesensor's coordinate frame.

In FIG. 4D, position and rotation of the sensor are represented ingenerator coordinates by a position vector r′={right arrow over (O′P′)}where O′ and P′ denote the magnetic center points of the generator andsensor, respectively, and where P′ is represented in the generator'scoordinate frame, having its origin at O′. The rotation of the sensor'scoordinate frame with respect to the generator's coordinate frame (e.g.,an angle of intersection between the x-axis of the sensor's coordinateframe and the x′-axis of the generator's coordinate frame) is defined bythe angle of rotation ψ′ measured from the x′-axis. Using polarcoordinates, the sensor's position and rotation may be defined byazimuth angle α′ measured from the x′-axis, the distance ρ′ (length ofr′), and ψ′, respectively, as defined with respect to the generator'scoordinate frame.

In some guidance and alignment implementations, the positionalrelationship between generator and sensor includes the position vector(e.g., r) but excludes the rotation angle (e.g., ψ). This partiallydefined positional relationship may apply, e.g., in a system where thedriver uses other information to align the vehicle 406 to the parkingstall frame as required for proper parking, e.g., by using roadmarkings, grass verges, curbstones, etc. as shown in FIG. 5.

In some other guidance and alignment implementations, the positionalrelationship excludes the parking sense of the vehicle (e.g., forward orreverse parking). This partially defined positional relationship mayapply in a system where the parking sense of the vehicle does not matter(e.g., because base and vehicle IPT couplers are center mounted) or, ifthe parking sense matters, the driver uses other information to park thevehicle in the right sense, e.g., from markings, signs, knowledge ofstandard installation rules, etc.

FIG. 6 illustrates a 3-axis magnetic field generator and a 3-axismagnetic field sensor based on an orthogonal arrangement of coils 602,604, 606, 612, 614, 616 in accordance with some implementations. Thecoils 602, 604, 606, 612, 614, 616 may be multi-turn wire loops with orwithout a magnetic core. The generator coils 602, 604, 606 are arrangedorthogonal to one another and are configured to be driven by respectivecurrents I_(x′), I_(y′) and I_(z′) to generate magnetic fields havingmagnetic moments in orthogonal directions, e.g., on a x′-, y′-, andz′-axis of the same generator coordinate frame previously described inconnection with FIGS. 4A-4D. The same is true for the sense coils 612,614, 616. If driven by respective currents, they would generate magneticmoments in orthogonal directions, e.g., on a x-, y-, and z-axis of thesensor's coordinate frame that may be arbitrarily rotated relative tothat of the generator, as previously described in connection with FIGS.4A-4D. In some implementations, the frequencies of oscillation of thecurrents I_(x′), I_(y′) and I_(z′) may be low enough such thatwavelengths of the magnetic fields generated by the generator coils 602,604, 606 are much larger than a distance separating the generator fromthe sensor. Moreover, dimensions of the generator coils 602, 604, 606and the sense coils 612, 614, 616 in the plane in which each is woundare much smaller than the distance separating the generator from thesensor. However, in operation, magnetic flux from the magnetic fieldsgenerated by the generator coils 602, 604, 606 may flow through thesense coils 612, 614, 616 (e.g., first sense coil 612, second sense coil614, and third sense coil 616) and generate respective voltages acrossthe terminals of each of the sense coils 612, 614, 616. For mathematicaltreatment, these voltage components may be written as a triple ofthree-dimensional vectors:

$\begin{matrix}{{V_{x^{\prime}} = \begin{bmatrix}V_{x^{\prime}x} \\V_{x^{\prime}y} \\V_{x^{\prime}z}\end{bmatrix}},\mspace{14mu}{V_{y^{\prime}} = \begin{bmatrix}V_{y^{\prime}x} \\V_{y^{\prime}y} \\V_{y^{\prime}z}\end{bmatrix}},\mspace{14mu}{V_{z^{\prime}} = \begin{bmatrix}V_{z^{\prime}x} \\V_{z^{\prime}y} \\V_{z^{\prime}z}\end{bmatrix}}} & (1)\end{matrix}$where V_(x′), V_(y′), V_(z′) denote the voltage vector produced by thefield generated by the x′-, y′-, and z′-generator coils 602, 604, 606,respectively.

The coil currents I_(x′), I_(y′), I_(z′) generating the three magneticmoments in the x′-, y′-, and z′-direction may be also represented invector form as:

$\begin{matrix}{{I_{x^{\prime}} - \begin{bmatrix}I_{x^{\prime}} \\0 \\0\end{bmatrix}},\mspace{14mu}{I_{y^{\prime}} = \begin{bmatrix}0 \\I_{y^{\prime}} \\0\end{bmatrix}},\mspace{14mu}{I_{z^{\prime}} = {\begin{bmatrix}0 \\0 \\I_{z^{\prime}}\end{bmatrix}.}}} & (2)\end{matrix}$Provided that the currents I_(x′), I_(y′), and I_(z′) generate magneticmoments of equal strength in all three orthogonal directions, Equation(3) may be assumed:I _(x′) =I _(y′) =I _(z′) =I  (3)

FIG. 7A illustrates a plurality of frequencies 700 for use infrequency-division magnetic field multiplexing, in accordance with someimplementations. As shown in FIG. 7A, in order to differentiate betweenthe magnetic field components generated by each of the generator coils602, 604, 606, each of the generator coils 602, 604, 606 may beconcurrently driven with currents oscillating at respective frequenciesf_(x′), f_(y′) and f_(z′), respectively. In some implementations,f_(x′), f_(y′) and f_(z′) may be equally spaced in frequency.

FIG. 7B illustrates a plurality of time slots 750 for use intime-division magnetic field multiplexing, in accordance with someimplementations. Time-division multiplexing schemes (TDM) may beutilized to generate magnetic field beacon signals with magnetic momentsin different axis directions. As opposed to frequency-divisionmultiplexing (FDM), magnetic field beacon signals may be generated andtransmitted sequentially in different time slots in a repetitivefashion. In some implementations, each of the generator coils 602, 604,606 are driven sequentially, during respective time slots. For example,time slots 712 a, 712 b, 712 c may be time slots during which thegenerator coil 602 (e.g., x′ coil) is driven, time slots 714 a, 714 b,714 c may be time slots during which the generator coil 604 (e.g., y′coil) is driven, and time slots 716 a, 716 b, 716 c may be time slotsduring which the generator coil 606 (e.g., z′ coil) is driven. A groupof time slots (e.g., time slots 712 a, 714 a, 716 a, respectivelydenoted as t_(x′), t_(y′) and t_(z′), for a 3-axis generator) of arepetition period may be called a frame. In some implementations, theframe duration may correspond to the position data update period of themagnetic field positioning system, e.g., 200 ms (5 position updates persecond). Frame synchronization of the magnetic field positioningreceiver may be achieved, e.g., by transmitting in-band asynchronization signal such as a pseudo-random sequence from time totime (see FIG. 24), temporarily omitting the ordinary beacon signaltransmissions, or out-of-band using a different carrier.

Alternatively, an extra time slot may be added to each frame forpurposes of frame synchronization. In some implementations of a 3-axisgenerator system, at least one of a x′-, y′- and z′-magnetic fieldsignal is transmitted in two time slots as illustrated in FIG. 7C. FIG.7C illustrates a plurality of time slots 780 for use in time-divisionmagnetic field multiplexing, in accordance with some otherimplementations. For example, time slots 782 a, 782 b, 784 a, 784 b maybe time slots during which the generator coil 602 (e.g., x′ coil) isdriven, time slots 786 a, 786 b may be time slots during which thegenerator coil 604 (e.g., y′ coil) is driven, and time slots 788 a, 788b may be time slots during which the generator coil 606 (e.g., z′ coil)is driven. The signal transmitted in time slot 782 a, 782 b (e.g.,t_(x′a)) may be used to mark the start of each frame. This signal maydiffer from the signals transmitted in the other time slots so as to bedistinguishable by the receiver as the start of a frame, even if it isaltered in some way by the transmission channel.

In some other implementations, some other multiplexed format may beutilized that allows separation of the voltage components induced intoeach of the three sense coils 612, 614, 616 (e.g., x, y, and z coilsrespectively). Other multiplexed formats may use: code divisionmultiplexing (CDM), frequency hopping, swept frequency, orthogonalfrequency division multiplexing (OFDM), or the like.

FIG. 8 illustrates a block diagram of a magnetic field position-findingsystem 800, in accordance with some implementations. The system 800comprises a 3-axis generator 802 configured to drive each of thegenerator coils 602, 604, 606 with respective current signals. Thesystem 800 additionally comprises a 3-axis sensor 804 configured toreceive a plurality of voltage signals from the sense coils 612, 614,616, where the voltage signals are induced in the sense coils 612, 614,616 by magnetic flux, generated by the generator coils 602, 604, 606passing though the sense coils 612, 614, 616.

Using a 3-axis generator 802 and a 3-axis sensor 804, as shown in FIG. 8for example, it is possible to determine a bi-ambiguous position and anon-ambiguous direction to the sensor from the generator's coordinateframe in the full 3D space up to a radius that is limited by theperformance characteristics of the system. However, this bi-ambiguitycannot be further resolved using information available in the sensedmagnetic field components.

This bi-ambiguity issue is illustrated by example in FIG. 9. FIG. 9illustrates magnetic moments m_(x′), m_(y′), m_(z′) of a magnetic fieldgenerated by a 3-axis generator (e.g., such as that shown in FIG. 8) andthe resulting magnetic field vector triples (H_(y′), H_(y′), H_(z′)) ateach of six different on-axis positions A′, B′, C′, D′, E′, F′, inaccordance with some implementations. The magnetic moment vectorsm_(x′), m_(y′), m_(z′) are illustrated at the origin of the generatorcoordinate frame O′=(0, 0, 0) and the resulting magnetic field vectortriples H_(x′), H_(y′), H_(z′) at the six equidistant on-axis pointsA′=(ρ, 0,0), B′=(0, ρ, 0), C′=(−ρ, 0,0), D′=(0, −ρ, 0), E′=(0,0, ρ),F′=(0,0, −ρ). At each of these six on-axis points, the vector triplecomprises a vector in a radial direction (e.g., H_(x′), for point A′)resulting from the on-axis moment and two other vectors (e.g., H_(y′),H_(z′) for point A′) in directions tangential to the radial directionsresulting from the two other magnetic moments pointing in perpendiculardirections. It can be seen that an ambiguous position always comprisestwo diametrically opposed (antipodal) positions, which may bemathematically expressed using position vectors in Equation (4) below:r′ ₁ =−r′ ₂  (4)

It can be shown that Equation (4) is also true for any off-axis position(not shown in FIG. 9). For each antipodal point pair there exists aunique vector triple that may be represented in terms of H-field vectorsH_(x′), H_(y′), H_(z′) or in terms of voltage vectors V_(x′), V_(y′),V_(z′) induced in the sense coils 612, 614, 616 assuming the sense coils612, 614, 616 are orthogonally placed. A vector triple forms atetrahedron that is defined by six quantities, e.g., the three voltagevector magnitudes, which may be expressed as scalar (dot) products|V_(x′)|=V_(x′)·V_(x′), |V_(y′)|=V_(y′)·V_(y′), |V_(z′)|=V_(z′)·V_(z′)and the three angles between the three voltage vectors as obtained fromthe three scalar products V_(x′)·V_(y′), V_(x′)·V_(z′), V_(y′)·V_(z·).

It is evident that these 6 quantities and thus the shape of thetetrahedron are invariant to any rotation of the three-axis sensor.Therefore, an antipodal position pair can be determined based on the 6quantities for any rotation of the sensor. The three vector magnitudes|V_(x)|, |V_(y′)|, |V_(z′)| alone can provide an ambiguous position withone solution in each octant and six of these position ambiguities can beresolved by using the sign of any two of the three scalar products, asshown in Table 1.

TABLE 1 Octant x′ y′ z′ V_(x′) · V_(y′) V_(x′) · V_(y′) V_(x′) · V_(y′)1 + + + + + + 2 − + + − + − 3 − − + + − − 4 + − + − − + 5 + + − + − − 6− + − − − + 7 − − − + + + 8 + − − − + −

For example, if the signs of V_(x′)·V_(y′) and V_(x′)·V_(z′) are bothpositive, the sensor is located either in octant 1 or octant 7. FromTable 1 it can be easily seen that the third scalar product(V_(y′)·V_(z′) in the example of Table 1) does not bring any moreinformation, thus it is redundant. However, it may be used to improve aposition estimate in the case of voltage vector corruption by noise.

The residual bi-ambiguity may be eliminated by using a physicalrestriction of the location of the sensor relative to the generator.Such a physical restriction may be z′>0, meaning that the system isconfigured to return only determinations where the sensor is located inthe z′>0 half space. In such implementations, any position exceptpositions on or near the x′-y′-plane where z′ is virtually zero may beprincipally determined unambiguously.

From FIG. 9 it can be easily seen that the residual bi-ambiguity of a3-axis generator and a 3-axis sensor positioning system cannot beresolved by restricting the direction (rotation) of the sensor, e.g.,φ′=0, θ′=0, ψ′=0, where φ′, θ′, and ψ′ denote the roll, pitch, andazimuth (yaw) rotation angles, respectively, of the sensor relative tothe generator's frame.

Moreover, the magnetic vector field patterns as obtained in a realmagnetic vectoring system for vehicle positioning may be significantlydistorted as compared to patterns obtained with ideal magnetic dipoles.Such distortion of the magnetic vector field pattern may occur if thesize of the generator coils 602, 604, 606 and/or the sense coils 612,614, 616 are similar to the distance between them. Presence of thevehicle metallic chassis (underbody structure), a conductive ground,e.g., a ferroconcrete ground, and any other large metallic structuresthat may be located in the path between generator and sensor may alsodistort the magnetic dipole field. Practical tests in real environmentshowever have shown that the basic field characteristics (field topology)resembles that of a dipole field and that the general findings onposition ambiguity and resolution disclosed and discussed herein arealso applicable to real vector fields. Though, special measures andalgorithms for position and direction finding will be required to copewith field distortion of real environments.

One difficulty associated with quasi-static magnetic field (e.g., nearfield) positioning techniques based on sensing an alternating magneticfield is the requirement for synchronization between the magnetic fieldgenerator and the magnetic field sensor. Absence of any synchronizationinformation may lead to a signal polarity ambiguity issue. Thoughrelated in some situations, this polarity ambiguity issue should not beconfused with the position ambiguity described above.

A magnitude, an orientation and a sense (polarity) may be attributed toa vector. Two vectors a and b may have equal length, equal orientationbut an opposite sense (polarity), e.g., a=−b. Orientation and sensetogether define the direction of a vector. Without supplementarysynchronization information it may be impossible to determine thepolarity of the sensed magnetic field vector in correct relation to thepolarity of the magnetic moment of the generating magnetic field, e.g.,as shown in FIG. 9. Polarity ambiguity is particularly an issue ofmagnetic field transmissions that are substantially unmodulated ornarrowband modulated sinusoidal (harmonic) carrier signals. Forsinusoidal carrier signals the polarity ambiguity may be called a180°-phase ambiguity.

The 180° phase ambiguity is one problem associated with the magneticradio compass, which has been used for radio direction finding, e.g., innautical and aeronautical navigation systems. FIG. 10A illustrates amagnetic radio compass 1000 using an x-y-oscilloscope, in accordancewith some implementations. The radio compass uses an oscilloscope todisplay bearing information. The concept of an “old” radio compass isused and described herein for solely explanatory purposes. FIG. 10Ashows sinusoidal voltage signals v_(x)(t) and v_(y)(t) as induced in andreceived from the x- and y-sense coils (e.g., the sense coils 612, 614)that may be expressed according to Equations (5) and (6):v _(x)(t)=V _(x) sin(ωt+δ _(x))  (5)v _(y)(t)=V _(y) sin(ωt+δ _(y))  (6)

The sinusoidal voltage signals v_(x)(t) and v_(y)(t) are connected tothe x- and y-channel of an oscilloscope so that they deflect the lightpoint on the screen in the x-direction and y-direction, respectively.V_(x) and V_(y) denote the peak amplitude of the x- and y-components,respectively, which are generally different from one another andproportional to the amplitudes of the x- and y-component of the magneticfield at the location of the sense coils 612, 614, assuming a homogenousfield distribution over the area of the sense coils.

The graph displaced on the screen of the scope and as perceived by thehuman eye is an ellipse. The ellipse is produced by the combined effectof the two deflecting signals v_(x)(t) and v_(y)(t) having the sameangular frequency ω but different phase angles in general (δ_(x)≠δ_(y)).This ellipse is also known as a Lissajous graph and results from asystem of parametric equations such as those given in Equations (5) and(6). For a perfect sense circuitry and oscilloscope the phase angles areequal (δ_(x)=δ_(y)) and the ellipse collapses into a straight linesegment. The long axis of the ellipse indicates the orientation of themagnetic field vector, provided that the terminals of the sense coilsand the inputs of the oscilloscope are connected in the correct order.More precisely, the long axis of the ellipse indicates the projection ofthe magnetic field vector onto the x, y plane of the sensor's coordinateframe, assuming a 3D vector having a z-component as well. However, asopposed to a classical compass that senses the earth's static magneticfield, the radio compass cannot reveal the polarity of the magneticfield vector and thus cannot determine its direction. Thetwo-dimensional (2D) magnetic radio compass concept may be extended to a3D radio compass concept using an x-y-z-oscilloscope (not shown in FIG.10A) and by additionally displaying the z-component, which may bedefined by Equation (7) below:v _(z)(t)=V _(z) sin(ωt+δ _(z))  (7)

Such a 3D radio compass would now display the image of an ellipsoid ofrotation whose long axis indicates the orientation of the magnetic fieldvector. Again, δ_(x)=δ_(y)=δ_(z) may be assumed for the ideal case, sothat the ellipsoid becomes a line segment with a certain length andorientation representing the magnetic field vector magnitude andorientation, respectively, in the sensor's coordinate frame. Still, themagnetic field vector polarity cannot be determined unless the sensorreceives external synchronization information, e.g., a time instant, aphase value or the half cycle period where the signal is valid to readthe polarity.

FIG. 10B illustrates a magnetic radio compass 1050 obtaining absolutephase information from a reference signal, in accordance with someimplementations. In theory, a sinusoidal time synchronization referencesignal v_(ref) (t) may be transmitted through a separate channel whosephase is not affected by the position and rotation of the sensor'scoordinate frame. Marking (or measuring) v_(x)(t) and v_(y)(t) atspecific time instances where the amplitude of the reference signal is,e.g., positive, as illustrated by the dashed lines and associatedcircles on the waveforms for v_(x)(t) and v_(y)(t) in FIG. 10B, wouldreveal the true polarity and thus the direction of the magnetic fieldvector.

In some other implementations, a robust in-band synchronization may beaccomplished using a magnetic field waveform whose induced voltagewaveform (derivative with respect to the time) is easily distinguishablefrom its inverted replica for any time shift and also if corrupted bynoise. Easily distinguishable may be quantified objectively by acorrelation coefficient, e.g., <0.5, for any time shift. FIG. 11A showsa non-sinusoidal transmission signal 1100 suitable for resolvingpolarity ambiguity, in accordance with some implementations. Using sucha signal 1100 (or a waveform having a similarly low correlationcoefficient with its inverted replica for any time shift) may allow thesystem to resolve signal polarity regardless of the sensor's position,rotation or exposure to noise. However, waveforms with this property arenon-sinusoidal which may be seen disadvantageous if there is onlylimited spectrum available for magnetic vectoring, e.g., 120-140 kHz,since such non-sinusoidal signals inherently comprise non-negligiblesignal energies in a wide range of harmonic frequencies.

In yet other implementations, the magnetic field transmissions may besinusoidal but a supplementary out-of-band reference signal at a carrierfrequency significantly higher than the magnetic field frequency istransmitted. FIG. 11B shows an amplitude-modulated reference signal 1150suitable for providing a receiver with synchronization information, inaccordance with some implementations. This reference signal 1150 may beamplitude modulated (AM) with a waveform that is equal to the sinusoidalmagnetic field transmission with respect to frequency and phase. Thoseskilled in the art will appreciate that the AM signal envelope remainslargely unaffected by the typical signal propagation effects and theposition and orientation of the antenna. The receiver may then employsimple envelope detection to obtain the required synchronizationinformation. However, the need for a modulated out-of-band referencesignal requiring extra hardware and antennas may be seen disadvantageouswith respect to system complexity, cost and the requirement foradditional frequency spectrum. Moreover, the available standard RF datacommunications may not be suitable for this purpose.

Analyzing the 3-axis generator/3-axis sensor problem, it has beendiscovered that the relative polarities between the three voltagevectors V_(x′), V_(y′), V_(z′) are only needed to resolve ambiguity thatis principally resolvable. A bi-ambiguous position can be determined bythe three vector magnitudes |V_(x′)|, |V_(y′)|, |V_(z′)| and the sign ofthe scalar product of two vector pairs as shown in Table 1 above. Whilethe magnitudes neither depend on the sensor's rotation nor on thevectors' polarity, the sign of the scalar products do. More precisely,they depend on the relative polarity of the vectors V_(x′) and V_(y′).The sign of the scalar product, e.g., V_(x′)·V_(y′) would change if thepolarity of one of the vectors was changed, e.g., (−)V_(x′)·V_(y′).However, it would not change if the polarity of both vectors waschanged, e.g., (−)V_(x′)·(−)V_(y′). Therefore, for a 3-axisgenerator/3-axis sensor system using sinusoidal transmissions, thereceiver only needs information about the relative phases between thex′-, y′- and z′-magnetic field signals (e.g., what the phases arerelative to one another rather than their absolute phases). Absolutephase information may not be needed. This however does not excludeimplementations where absolute phase information is used, e.g., toimprove a position estimate in the presence of noise.

Provided that a relative phase relationship between the three signals isestablished, flipping the polarity of all signals, e.g., as would existfor a 180° absolute phase ambiguity, would result in the same positionestimate. Changing all signal polarities at the same time may be seen asmirroring an entire vector triple forming a mirrored tetrahedron. It canbe shown that there exists no position pair in a 3D space where thevector triples, as produced at a first position, is a mirrored versionof the vector triple at a second position. Moreover, a mirrored vectortriple cannot be produced by any rotation of the sensor about any axis.This is analogous to a right hand 3D coordinate frame that cannot bechanged into a left hand 3D frame by rotation. However, this may notnecessarily always be true for a 2-axis generator/3-axis sensor system,as will be described below.

The difference between relative and absolute phase (polarity)synchronization can be illustrated using the concept of the “old” radiocompass as shown in FIG. 12. FIG. 12 illustrates a magnetic radiocompass 1200 displaying orientations of two magnetic field vectors, inaccordance with some implementations. As opposed to the radio compassillustrated in FIG. 10A, the radio compass of FIG. 12 uses afour-channel oscilloscope connected to an analog circuitry having fouroutputs. The analog circuitry separates and amplifies the voltagesignals v_(x′x)(t) and v_(y′,x)(t) as induced into the x-sense coil(e.g., the coil 612) by the x′- and y′-magnetic field, respectively, asgenerated, e.g., at different frequencies. Likewise, this analogcircuitry separates and amplifies the voltage signals v_(x′,y)(t) andv_(y′,y)(t) as induced into the y-sense coil (e.g., the coil 614) by thex′- and y′-magnetic field, respectively. The four channel oscilloscopeis configured such that signals v_(x′,x)(t) and v_(y′,x)(t) deflect thelight point in the x-direction and the signals v_(x′,y)(t) andv_(y′,y)(t) in the y-direction. If correctly wired, the displayed graph,as perceived by the human eye, indicates orientation of the x′- andy′-magnetic field vectors, separately, and more precisely theirprojection onto the x, y-plane, since the z-component is ignored.

In the absence of any supplementary synchronization information, the2-signal radio compass 1200 is not able to indicate a direction(polarity) of either of the two vectors. Since each vector has anambiguous polarity, there exist four possible combinations ofdirections, as illustrated in FIG. 13. FIG. 13 shows the differentcombinations 1300 of magnetic vector polarity that may be resolved withsupplementary synchronization information, in accordance with someimplementations. FIG. 13 shows a case A, a case B, a case C, and a caseD and uses circles to mark the heads of the two vectors previouslydescribed in connection with FIG. 13. Providing the radio compass 1200with absolute phase information, the Lissajous graphs shown in each ofcases A-D are marked in a manner such that all four cases can bedistinguished. However, providing only relative phase information wouldstill allow differentiation of case A from cases B and D but not fromcase C, for example. In other words, relative phase information allowsthe differentiation of those vector pairs that have an acute angle(ϑ<90°) from those that have an obtuse angle (ϑ>90°) between thevectors. Vector theory provides that an acute angle and an obtuse angleare equivalent to a positive scalar product and a negative scalarproduct, respectively. The sign of the scalar product and thereforerelative phase (polarity) information suffices to resolve an ambiguousposition between an acute angle and an obtuse angle between vectors at afirst position and at a second position, respectively.

Different synchronization requirements may apply for a 2-axisgenerator/2-axis sensor or for a 3-axis generator/2-axis sensor system,as will be discussed below. In such configurations, knowledge of theabsolute phase can help to resolve ambiguities, which will be shown forthe application of vehicle positioning for wireless charging. FIG. 14displays field lines of a magnetic field 1400 generated by a 2-axismagnetic field generator having magnetic moments m_(x′) and m_(y′) inaccordance with some implementations. FIG. 14 also displays magneticvector pairs present at 4 on-axis positions and 4 off-axis positions.The field pattern shown refers to a cut plane that is parallel to thex′-y′-plane and offset by a height z′₀>0. In some use cases of vehiclepositioning, the x′-y′-plane may be considered the ground (or floor) andthe offset plane at z′₀ the horizontal plane where the vehicle mountedsensor is located and in which it is moving. The magnetic moments m_(x′)and m_(y′) may refer to the magnetic moments of x′- and y′-generatorcoils 602, 604, respectively, as integrated into a base pad.

FIG. 14 also shows the horizontal (x′-, y′-) components of the magneticfield vectors H_(x′) and H_(y′) of the x′-, y′-magnetic field,respectively, as well as the angle ϑ between the two vectors at 8selected points. The encircled ± sign indicates the sign of the vector'sz′-component that is perpendicular to the x′-y′-plane. A + signindicates a z′-component extending out the front of the page, while asign indicates a z′-component extending out the back of the page. The 8selected points comprise four on-axis points designated A′, B′, C′, D′at equal distances from the origin O′ and four off-axis points E′, F′,G′, H′ also the same distances from the origin O′ and pairwise antipodal(e.g., diametric). As it can be seen in FIG. 14, vector pairs at on-axispoints form an angle ϑ=90°, while vector pairs at off-axis points showpairwise either an acute or obtuse angle (e.g., less than 90° and morethan 90°, respectively). For the vehicle application, there are normallyonly three degrees of freedom for movement: the x′-y′-position and theazimuth (yaw) rotation angle ψ′, hence the following physicalrestrictions for the sensor's coordinate frame may apply:z′≅z′ ₀>0φ′≅0θ′≅0where φ′≅0 and θ′≅0 refer to the vehicle's roll and pitch angles,respectively, which may be considered substantially zero.

By inspecting FIG. 14 it can be found that an unambiguous position canbe determined using a 2-axis generator/3-axis sensor system, providedthat the above physical restrictions apply. Non-antipodal vector pairscan be distinguished by the vectors' magnitudes |H_(x′)|, |H_(y′)|and/or by the angle ϑ, while the antipodal vector pairs whose horizontalcomponents (e.g., H_(x′) and H_(y′)) are the same can be distinguishedby their vertical (z′-)component. It can also be found that distinctionis possible for any azimuthal rotation ψ′ of the sensor with respect tothe generator, provided that the vector's true direction (polarity) canbe determined, e.g., based on absolute phase information. It can befound that no vector pair matches another vector pair if rotated by anyazimuth angle ψ′ due to the z′-component.

FIG. 15 illustrates vector polarity ambiguity in a system 1500 using a2-axis generator and only relative phase synchronization, in accordancewith some implementations. In FIG. 15 vector polarity is ambiguous, asindicated by the double-arrows in opposite directions. Using thisrepresentation, it becomes evident that one vector pair matches anothervector pair at the antipodal point when rotated by ψ′=180°. Hence thereis a bi-ambiguity, e.g., position A′ cannot be distinguished from C′.Without absolute phase information, this bi-ambiguity can only beresolved by introducing a further physical restriction either on thesensor's position, e.g., x′<0, or the sensor's rotation, e.g.,−90°<ψ′<90°. In some applications of vehicle positioning there may be noneed for resolving this bi-ambiguity. This may be true for systems that,for purposes of guidance and alignment, displays the position of thecharging spot as seen from the vehicle, e.g., on a dashboard display.For such park assist applications, it may be acceptable that userscannot distinguish the two scenarios.

FIGS. 16A and 16B show vehicle parking scenarios 1600, 1650 thatillustrate position and rotation ambiguity in a system using a 2-axisgenerator and only relative phase synchronization, in accordance withsome implementations. FIG. 16A shows two positions of the vehicle 406with respect to the base pad 402: at point A′ heading essentiallytowards the base pad 402 (|ψ′|<90°), and at antipodal position C′heading essentially towards the base pad 402 (|ψ′|>90°). As per theabove discussion, the vehicle 406 being located at either of points A′or C′ would appear the same on an alignment display. However, in FIG.16B, the user would get a different view for the two points A′ and C′.Being able to distinguish between the ambiguous scenario of FIG. 16A andthe ambiguous scenario of FIG. 16B is actually most important since theuser needs to know whether a position of optimal alignment is located infront of (e.g., as in FIG. 16A) or behind (e.g., as in FIG. 16A) thevehicle 406 with respect to a forward direction of motion of the vehicle406. This distinction is possible with only relative phasesynchronization (as opposed to absolute phase synchronization) as longas the z′-component of the magnetic field can be sensed. This conceptmay be considered a partially defined positional relationship asdescribed above where the driver cares about the direction of thevehicle 406 relative to the base pad 402 and thus relative to theparking stall.

Relative phase synchronization between the different magnetic fieldsignals may be less demanding and less critical than absolute phasesynchronization. This may be especially true if the system usessinusoidal frequency multiplexed magnetic field transmissions and ifout-of-band synchronization signaling is not an option. Using sinusoidal(e.g., multi-tone) transmissions can provide a system with lowcomplexity, high spectral efficiency, and large dynamic range, e.g., tocope with the so-called “near-far” effects as are common for magneticfield transmissions that follow a third-power distance law (e.g., wheremagnetic field strength is proportional to the third power of thedistance).

In a system using multi-tone signals, absolute phase synchronization mayrequire timing accuracy of within a fraction of the cycle period, whilerelative phase synchronization may require a lower accuracy of withinmultiple cycle periods, depending on the actual frequency separation ofthe transmitted tones, the signal-to-noise ratio, and othersynchronization requirements. This can be explained by the fact that therelative phase Δφ between a signal with angular frequency ω₁ and asignal with angular frequency ω₂ evolves much slower than the absolutephase φ, provided that the angular frequency difference |Δω|=|ω₁−ω₂| ismuch smaller than ω₁ or ω₂. This may be expressed mathematical terms, asshown in Equation 8.Δφ(t)=|Δω|t<<φ(t)=|ω₁ |t for any t≠0.  (8)

Since phases of the two signals evolve differently over time,determining a relative phase (relative polarity) between sinusoidalsignals with different frequencies can only be performed at certaintimes and more precisely, during certain time intervals, which reoccurperiodically. This is illustrated by the graph 1700 in FIG. 17, whichdisplays the phase difference Δφ of a double-tone signal as a functionof time, in accordance with some implementations. Displaying thetime-function of the relative phase Δφ(t) in the form of (Δφ(t) mod2π)−π, where mod denotes the modulo function. FIG. 17 shows that therelative phase Δφ(t) periodically returns to the same value, e.g., Δφ=0with a period of

$\frac{2\;\pi}{\Delta\;\omega}.$

In the following, relative phase synchronization will now be furtherdiscussed by assuming two sinusoidal signals with different angularfrequencies and unknown polarity expressed by their peak amplitudes(±)A₁ and (±)A₂ and complex signal representation, as shown in Equations(9) and (10).s ₁(t)=(±)A ₁ exp(jω ₁ t),  (9)s ₂(t)=(±)A ₂ exp(jω ₂ t).  (10)

The relative polarity may be obtained from the sign of the product ofs₁(t) and the conjugate complex of s₂(t) expressed as shown in Equation(11).sign( s ₁(t _(s))· s ₂*(t _(s)))  (11)at times, t_(s), in periodically occurring intervals with a durationdepending on the synchronization accuracy as required for a particulartransmission scheme, choice of frequencies and the channel SNR.

Assuming an infinite SNR, the periodicity of times t_(s) in Equation(11) may be as large as that defined by the inequality of Equation (12)below:

$\begin{matrix}{{e\left( {{- j}\frac{\pi}{2}} \right)} < {{e\left( {j\;\omega_{1}t_{s}} \right)} \cdot {e\left( {{- j}\;\omega_{2}t_{s}} \right)}} < {{e\left( {j\frac{\pi}{2}} \right)}.}} & (12)\end{matrix}$

We can define the phase difference Δφ(t_(s)) by using the modulofunction as shown in Equation (13), and using Equation (12), Equation(13) may be simplified to Equation (14):

$\begin{matrix}{{\Delta\;{\varphi\left( t_{s} \right)}} = {{{\varphi_{1}\left( t_{s} \right)} - {\varphi_{2}\left( t_{s} \right)}} = {{\left( {\omega_{1}t_{s}{mod}\; 2\;\pi} \right) - \left( {\omega_{2}t_{s}{mod}\; 2\;\pi} \right)} = {\Delta\;\omega\; t_{s}{mod}\; 2\;\pi}}}} & (13) \\{\mspace{79mu}{{{\Delta\;{\varphi\left( t_{s} \right)}}} < {\frac{\pi}{2}.}}} & (14)\end{matrix}$

In low SNR conditions, the absolute value of the tolerable phasedifference Δφ_(max) may be only a fraction of

$\frac{\pi}{2}$Thus, the range for the tolerable phase difference Δφ_(max) may beexpressed as Equation (15) below:

$\begin{matrix}{{{\Delta\;{\varphi\left( t_{s} \right)}}} < {\Delta\;\varphi_{\max}} < \frac{\pi}{2}} & (15)\end{matrix}$

Based on Equation (15) the times t_(s) where the relative polaritybetween s ₁(t) and s ₂(t) can be determined may be expressed as shown inEquation (16) below:

$\begin{matrix}{{t_{s} = {{n\frac{2\;\pi}{\Delta\;\omega}} + {\delta\; t_{s}}}};\mspace{14mu}{n \in {\mathbb{N}}}} & (16)\end{matrix}$where δt_(s) denotes the synchronization error tolerance having valuesas permitted according to Equation (17) below:

$\begin{matrix}{\frac{{- \Delta}\;\varphi_{\max}}{\Delta\;\omega} < {\delta\; t_{s}} < \frac{\Delta\;\varphi_{\max}}{\Delta\;\omega}} & (17)\end{matrix}$

Equation (16) defines time intervals occurring periodically at times

${n\frac{2\pi}{\Delta\;\omega}},$with n∈

. For virtually zero tolerance (δt_(s)≅0), the relative polarity canonly be determined at periodic distinct time instances that satisfyEquation (18) below.

$\begin{matrix}{{t_{s} = {n\frac{2\pi}{\Delta\;\omega}}};{n \in {\mathbb{N}}}} & (18)\end{matrix}$

In some implementations, a double-tone signal is used to generate atleast one of the x′-, y′- and z′-magnetic fields of a three-axisgenerator system. Choosing the x′-field for the double tone transmissionas an example, the double-tone excitation current i_(x′)(t) may beexpressed by Equation (19) below:i _(x′)(t)=I _(x′a) sin(ω_(x′a) t)+I _(x′b) sin(ω_(x′b) t)  (19)where I_(x′a), I_(x′b) denote the peak amplitudes and ω_(x′a) andω_(x′b) the angular frequencies of tone “a” and tone “b”, respectively.Assuming a single-tone transmission for the other magnetic fieldtransmissions, the excitation currents to generate the y′- and z′-fieldmay be expressed by Equations (20) and (21) below:i _(y′)(t)=I _(y′) sin(ω_(y′) t),  (20)i _(z′)(t)=I _(z′) sin(ω_(z′) t).  (21)

Since both tones of the double-tone transmission are equally affected bythe transmission channel and thus by the position and rotation of thesensor, the positioning receiver may use this at least one double-tonesignal to derive synchronization information as needed to establishrelative phase synchronization between the x′-, y′- and z′-magneticfield transmissions. This synchronization information may comprise timeinstances and time intervals for t_(s) as defined by (16)-(18).

Since the x′-field is generated by a double-tone, in someimplementations, the amplitudes I_(x′a) and I_(x′b) may be reduced by afactor of √{square root over (2)} so that the three generated magnetic(sum) moments have equal r.m.s. amplitudes.

In some implementations, tone frequencies are chosen such that adjacenttone frequencies are separated by Δω and the frequencies of the at leastone double-tone are adjacent to one another. Using the exemplaryfour-tone scheme as given by (19)-(21) and the above described selectionof tone frequencies, the set of tone frequencies described by Equations(22)-(24) may be obtained:ω_(x′b)=ω_(x′a)+Δω  (22)ω_(y′)=ω_(x′b)+Δω=ω_(x′a)+2Δω  (23)ω_(z′)=ω_(y′)+Δω=ω_(x′a)+3Δω  (24)The angular frequency spacing Δω may have a positive or a negativevalue. Assuming perfect receiver synchronization at time instances t_(s)as defined by (16)-(18) and using complex signal representation, the setof voltages induced, e.g., into the x-sense coil (e.g., the sense coil612) at the different transmission frequencies may be expressedaccording to Equations (25)-(28):

$\begin{matrix}{\mspace{79mu}{{{\underset{\_}{V}}_{x^{\prime}{ax}}\left( t_{s} \right)} = {{V_{x^{\prime}{ax}}{\exp\left( {j\;\omega_{x^{\prime}a}t_{s}} \right)}} = {V_{x^{\prime}{xa}}{\exp\left( {j\; n\frac{2\pi}{\Delta\;\omega}\omega_{x^{\prime}a}} \right)}}}}} & (25) \\{{{\underset{\_}{V}}_{x^{\prime}{bx}}\left( t_{s} \right)} = {{V_{x^{\prime}{bx}}{\exp\left( {j\;\omega_{x^{\prime}a}t_{s}} \right)}{\exp\left( {j\;\Delta\;\omega\; t_{s}} \right)}} = {V_{x^{\prime}{xb}}{\exp\left( {j\; n\frac{2\pi}{\Delta\;\omega}\omega_{x^{\prime}a}} \right)}}}} & (26) \\{{{\underset{\_}{V}}_{y^{\prime}x}\left( t_{s} \right)} = {{V_{y^{\prime}x}{\exp\left( {j\;\omega_{x^{\prime}a}t_{s}} \right)}{\exp\left( {j\; 2\Delta\;\omega\; t_{s}} \right)}} = {V_{y^{\prime}x}{\exp\left( {j\; n\frac{2\pi}{\Delta\;\omega}\omega_{x^{\prime}a}} \right)}}}} & (27) \\{{{\underset{\_}{V}}_{z^{\prime}x}\left( t_{s} \right)} = {{V_{z^{\prime}x}{\exp\left( {j\;\omega_{x^{\prime}a}t_{s}} \right)}{\exp\left( {j\; 3\Delta\;\omega\; t_{s}} \right)}} = {V_{z^{\prime}x}{\exp\left( {j\; n\frac{2\pi}{\Delta\;\omega}\omega_{x^{\prime}a}} \right)}}}} & (28)\end{matrix}$with time index n∈

.

Multiplying the four phasors by

$\exp\left( {{- j}\; n\frac{2\pi}{\Delta\;\omega}\omega_{x^{\prime}a}} \right)$rotates them all onto the real axis finally yielding the x-component ofthe x′-, y′- and z′-voltage vectorsV _(x′x)(t _(s))=V _(x′ax) +V _(x′bx)  (29)V _(y′x)(t _(s))=V _(y′x)  (30)V _(z′x)(t _(s))=V _(z′x)  (31)

Optimum choice of the angular frequency separation Δω of the multi-tonetransmission, which is related to the signal filtering requirements ofthe receiver, is another aspect of this disclosure. In a real systemwhere received signals are typically noisy and where there may bemultiple magnetic field transmissions at a plurality of frequencies, itis desirable that received tone signals be optimally filtered. Theminimum filter bandwidth is mainly dictated by a sampling rate that maybe given by the position update rate 1/T_(p) (the number of positionvalues the positioning receiver needs to compute per unit time). Forpositioning applications in stationary wireless electric vehiclecharging, a suitable position update rate may be 10 updates per second.

According to the uncertainty principle, position update rate and minimumfilter bandwidth are related. For a Gaussian-shaped filter impulseresponse, the pulse width in time may be defined as twice the standarddeviation of the Gaussian pulse T_(F)=2σ_(t) and the pulse (band) widthas B_(F)=2σ_(ƒ) accordingly, the time-bandwidth product is constrainedby Equation (32):T _(F) ·B _(F)=2σ_(t)·2σ_(ƒ)≤2  (32)Assuming the pulse width T_(F)=T_(p) with T_(p) the sample (positionupdate) period provides for a minimum filter bandwidth, according toEquation (33):

$\begin{matrix}{B_{F} = {\frac{2}{T_{F}} = {20\mspace{14mu}{Hz}}}} & (33)\end{matrix}$

For the example of a Gaussian filter and T_(p)= 1/10s, the minimumbandwidth becomes B_(F)=20 Hz.

Other factors to consider are tone frequency errors due to oscillatorinstability and thermal drifts. These effects may require a somewhatlarger filter bandwidth than the above-calculated theoretical values.

To get enough frequency selectivity, larger frequency separation thangiven by the filter bandwidth B_(F) may be needed to avoid cross-talkfrom adjacent frequency tones. A minimum frequency separation betweentones of the same positioning transmitter may be Δƒ≥5 B_(F) (100 Hz inthe example given above). About 10 B_(F) (200 Hz in the example givenabove) may be required between adjacent frequency tones of differentpositioning transmitters (different magnetic beaconing channels).

Other filter functions may be used instead of the Gaussian function. Anyfunction known as a window function for spectral analysis, e.g., arectangular window, a Hanning window, a Kaiser-Bessel window, aBlackman-Harris window, etc. may be used. Some windows, e.g., theBlackman-Harris window, can provide very high attenuation of adjacentfrequency tone signals, provided that there is enough frequencyseparation between them.

In one system, the positioning receiver may use a bank of synchronousdetectors to filter and detect each of the complex voltage components ofeach transmitted tone as received by each sense coil. FIG. 18illustrates a block diagram of a synchronous detector 1800 of a magneticfield positioning receiver, in accordance with some implementations. Thesynchronous detector 1800 may be configured to filter and detect thetone transmitted at angular frequency ω_(x′a), as received by thex-sense coil (e.g., the sense coil 612). The synchronous detector 1800provides at its two outputs the real and imaginary parts (I-componentand Q-component), respectively, of the complex voltage V _(x′ax)=Re{V_(x′ax)}+jIm{V _(x′ax)}.

The synchronous detector 1800 comprises a quadrature mixer(down-converter) and first and second integrators 1806, 1808,respectively. The quadrature mixer comprises a first mixer 1802configured to multiply the input signal by sin(ω_(x′a)t) to provide theI-component, and a second mixer 1804 configured to multiply the inputsignal by cos(ω_(x′a)t) to provide the Q-component. The outputs of thefirst and second mixers 1802, 1804 are input to the first and secondintegrators 1806, 1808, respectively. Both integrators 1806, 1808perform the same function as a FIR low pass filter by weighing thebaseband signal with the filter impulse response (window function) w(t).Integration is carried out at a rate of 1/T_(p) over the time intervalindicated by Equation (34):nT _(p) −T _(w)/2<t≤nT _(p) +T _(w)/2  (34)with nT_(p), n∈

defining the center time of the stepwise moving integration interval.The integrators deliver one complex output value every T_(p) seconds.The integration time is the length T_(w) of the filter function w(t).Consecutive integration intervals may overlap if T_(w)>T_(p).

In a system in accordance with the present application, filtering anddetection is performed quasi-synchronously with respect to the tonefrequency but asynchronously with respect to the transmitter's time,which is denoted by t′ below. There may be an arbitrary (random) timeoffset T₀ between the transmitter's time base and the receiver's timebase and also a small relative time drift defined by a coefficient (γclose to 1) as a consequence of inaccuracy associated with thetransmitter's and receiver's reference clocks. The relationship betweentransmitter's and receiver's time bases may be expressed as shown inEquation (35):t′=γt−T ₀  (35)

Using Equation (35), definitions made above, and complex signalrepresentation, the operation of the synchronous detector as shown inFIG. 18 may be expressed according to Equation (36):

$\begin{matrix}{{\underset{\_}{V}}_{x^{\prime}{ax}} = {\int_{{nT}_{p} - T_{w/2}}^{{nT}_{p} + T_{w/2}}{{w\left( {t - {nT}_{p}} \right)}{{{\underset{\_}{v}}_{x}\left( t^{\prime} \right)} \cdot {\exp\left( {{- j}\;\omega_{x^{\prime}a}t} \right)}}\ {dt}}}} & (36)\end{matrix}$

Assuming the set of tone signals as defined by Equations (19)-(21) andabsence of any noise component, the input signal as delivered by thex-sense coil 612 may be defined according to Equation (37):v _(x)(t′)= v _(x′ax)(t′)+ v _(x′bx)(t′)+ v _(y′x)(t′)+ v _(z′x)(t′)  (37)

Furthermore, assuming that the synchronous detector 1800 sufficientlysuppresses signals with angular frequency ω≅ω_(x′a), only v _(x′ax)(t′)is retained. Substituting (36) for the time variable t′, the relevantinput signal may be expressed by Equation (38):v _(x′ax)(t′)=V _(x′ax) exp(jω _(x′a) t′)=V _(x′ax) exp(jω _(x′a)γt)exp(−jω _(x′a) T ₀)  (38)

Substituting (38) in (36), yields the complex output (detected voltagephasor) of the synchronous detector, expressed by Equation (39):

$\begin{matrix}{{\underset{\_}{V}}_{x^{\prime}{ax}} = {{\int_{{nT}_{p} - T_{w/2}}^{{nT}_{p} + T_{w/2}}{{w\left( {t - {nT}_{p}} \right)}{{{\underset{\_}{v}}_{x^{\prime}{ax}}\left( t^{\prime} \right)} \cdot {\exp\left( {{- j}\;\omega_{x^{\prime}a}t} \right)}}\ {dt}}} = {V_{x^{\prime}{ax}}{\exp\left( {{- j}\;\omega_{x^{\prime}a}T_{0}} \right)}{\int_{{nT}_{p} - T_{w/2}}^{{nT}_{p} + T_{w/2}}{{w\left( {t - {nT}_{p}} \right)}{\exp\left( {j\;{\omega_{x^{\prime}a}\left( {\gamma - 1} \right)}t} \right)}\ {dt}}}}}} & (39)\end{matrix}$

Using the assumptions of γ≅1 and a normalized filter function w(t),

$\begin{matrix}{{\int_{{nT}_{p} - T_{w/2}}^{{nT}_{p} + T_{w/2}}{{w\left( {t - {nT}_{p}} \right)}{dt}}} = 1} & (40)\end{matrix}$and some rearrangements, equation (39) may be simplified to Equation(41) below:V _(x′ax) ≅V _(x′ax) exp(−jω _(x′a) T ₀)exp(−jω _(x′a)(1−γ)nT_(p))  (41)

The noise-free outputs of the other synchronous detectors connected tothe x-sense coil 612 may be obtained accordingly, as expressed inEquations (42)-(44) below:V _(x′bx) ≅V _(x′bx) exp(−jω _(x′b) T ₀)exp(−jω _(x′b)(1−γ)nT_(p))  (42)V _(y′x)≅(±)V _(y′x) exp(−jω _(y′) T ₀)exp(−jω _(y′)(1−γ)nT _(p))  (43)V _(z′x)≅(±)V _(z′x) exp(−jω _(z′) T ₀)exp(−jω _(z′)(1−γ)nT _(p))  (44)

Expressions above show three terms: a magnitude, a constant phase angleand a stepwise rotating phasor that evolves as time index n increments.The constant phase offset can be attributed to the relative time offsetT₀, while the rotating phasor to the relative time drift that manifestsin a small relative frequency offset.

As opposed to the expressions for V _(x′ax) in Equation (41) and V_(x′bx) in Equation (42), a polarity uncertainty (±) has been introducedin the expressions for V _(y′x) in Equation (43) and V _(z′x) inEquation (44). This polarity uncertainty shall be understood as arelative polarity uncertainty between the V _(x′ax) or V _(x′bx) and V_(y′x) and between V _(x′ax) or V _(x′bx) and V _(z′x). There is norelative polarity uncertainty between V _(x′ax) and V _(x′bx) bydefinition, since these components are obtained from the double-tonesignal as transmitted via the x′-magnetic field and, thus, are equallyaffected by the transmission channel.

In some implementations, the receiver performs relative phasesynchronization by first determining the phase difference (relativephasor) between phasors V _(x′ax) and V _(x′bx) and second by correcting(rotating) all output phasors by an angle given by the relative phasor.It will be shown further down that this operation of phase correction isequivalent to adjusting the receiver's timing as defined, e.g., byEquations (16), (17).

The receiver derives the phase difference (relative phasor) at leastfrom output phasors V _(x′ax) and V _(x′bx) by using the followingcomplex phasor operation expressed by Equation (45):

$\begin{matrix}{{\exp\left( {j} \right)} = \frac{{\underset{\_}{V}}_{x^{\prime}{bx}} \cdot {\underset{\_}{V}}_{x^{\prime}{ax}}^{*}}{{{\underset{\_}{V}}_{x^{\prime}{bx}} \cdot {\underset{\_}{V}}_{x^{\prime}{ax}}^{*}}}} & (45)\end{matrix}$which may be considered as the normalized scalar product in complexnumber notation. Substituting (41) and (42) into (45) and somemanipulations provides an expression for the relative phasor in timeinterval n, according to Equation (46):exp(

_(n))≅exp(−j(ω_(x′b) −jω _(x′a))T ₀)·exp(−j(ω_(x′b) −jω _(x′a))(1−γ)nT_(p))  (46)Using the definition of Δω of Equations (22)-(24), equation (46) may berewritten as shown in Equation (47):exp(j

_(n))≅exp(−jΔωT ₀)·exp(−jΔω(1−γ)nT _(p))≅exp(−jΔω(T ₀+(1−γ)nT_(p)))  (47)The term (1−γ)nT_(p) represents the timing drift of the receiver's timebase relative to the transmitter's time base. Since 1−γ is typically avery small factor (e.g., ±100 ppm) this timing drift may be consideredminor so that the relative phasor stays nearly constant as timeadvances.

In some implementations, the receiver applies the estimated relativephasor to all synchronous detector outputs to achieve relative phasesynchronization. For the exemplary tone frequency definitions ofEquations (22)-(24), this may be accomplished by multiplying detectoroutput V _(x′bx) by exp(−j

_(n)), detector output V _(y′x) by (exp(j

_(n)))², and detector output V _(z′x) by (exp(−j

_(n)))³ as shown in the following:

Using equation (47) and the exemplary definitions of equations(22)-(24), relative phase correction of the component V f_(bx) may beexpressed as shown in Equation (48).V _(x′bx)·exp(−j

_(n))≅V _(x′bx)·exp(−jω _(x′a)(T ₀+(1−γ)nT _(p)))·exp(−jΔω(T ₀+(1−γ)nT_(p)))·exp(jΔω(T ₀+(1−γ)nT _(p)))≅V _(x′bx)·exp(−jω _(x′a)(T ₀+(γ−1)nT_(p)))  (48)

Accordingly, relative phase corrections of components V _(y′x) and V_(z′x) become equations (49)-(50), respectively.V _(y′x)·(exp(−j

_(n)))²≅(±)V _(y′x)·exp(−jω _(x′a)(T ₀+(1−γ)nT _(p)))·exp(−j2Δω(T₀+(1−γ)nT _(p)))·exp(j2Δω(T ₀+(1−γ)nT _(p)))≅(±)V _(y′x)·exp(−jω_(x′a)(T ₀+(1−γ)nT _(p)))  (49)V _(z′x)·(exp(−j

_(n)))²≅(±)V _(z′x)·exp(−jω _(x′a)(T ₀+(1−γ)nT _(p)))·exp(−j3Δω(T₀+(1−γ)nT _(p)))·exp(j3Δω(T ₀+(1−γ)nT _(p)))≅(±)V _(z′x)·exp(−jω_(x′a)(T ₀+(1−γ)nT _(p)))  (50)

Equations (48) to (50) show that resulting (phase corrected) outputphasors including V _(x′ax) are all equally oriented (but notnecessarily equally directed) in the complex plane and are rotatingquasi-phase synchronously as time advances and if γ≠0.

In the following it will be shown that relative phase correction isequivalent to time synchronization in accordance with (16), (17), and(25)-(28). Considering the complex output of the synchronous detector asthe Fourier transform of the windowed time-domain input signal v_(x′ax)(t′) at the distinct frequency ω_(x′a) and using (38) providesequation (51):

$\begin{matrix}{{{\underset{\_}{V}}_{x^{\prime}{ax}}\left( \omega_{x^{\prime}a} \right)} = {{\int_{{- {nT}_{p}} - T_{w/2}}^{{nT}_{p} + T_{w/2}}{{{w\left( {t - {nT}_{p}} \right)} \cdot {{\underset{\_}{v}}_{x^{\prime}{ax}}\left( t^{\prime} \right)} \cdot {\exp\left( {{- j}\;\omega_{x^{\prime}a}t} \right)}}\ {dt}}} = {{dt} = {\int_{{- {nT}_{p}} + T_{w/2}}^{{nT}_{p} + T_{w/2}}{{{w\left( {t - {nT}_{p}} \right)} \cdot V_{x^{\prime}{ax}}}{{\exp\left( {j\;\omega_{x^{\prime}a}t^{\prime}} \right)} \cdot {\exp\left( {{- j}\;\omega_{x^{\prime}a}t} \right)}}{dt}}}}}} & (51)\end{matrix}$

The variable t′ as defined in (35) may be rewritten in the form of atime shift τ_(s) that is a function of t according to equation (52):t′=γt−T ₀ =t−(T ₀+(1−γ)t)=t−τ _(s)(t)  (52)

Over the limited integration interval [−nT_(p)+T_(w)/2, nT_(p)+T_(w)/2],the input signal v _(x′ax)(t′) may be considered as non-drifting butsolely shifted in time by:τ_(s)(nT _(p))=T ₀+(1−γ)nT _(p)  (53)

Substituting (53) in (52) and (52) in (51) and applying the shifttheorem of Fourier transforms provides equation (54):

$\begin{matrix}{{{{\underset{\_}{V}}_{x^{\prime}{ax}}\left( \omega_{x^{\prime}a} \right)}{\int_{{- {nT}_{p}} - T_{w/2}}^{{nT}_{p} + T_{w/2}}{{{w\left( {t - {nT}_{p}} \right)} \cdot {{\underset{\_}{v}}_{x^{\prime}{ax}}\left( {t - {\tau_{s}\left( {n\; T_{p}} \right)}} \right)} \cdot \exp}\left( {{- j}\;\omega_{x^{\prime}a}t} \right)\ {dt}}}} = {{\exp\left( {{- j}\;\omega_{x^{\prime}a}{\tau_{s}\left( {nT}_{p} \right)}} \right)} \cdot {\int_{{- {nT}_{p}} + T_{w/2}}^{{nT}_{p} + T_{w/2}}{{{w\left( {t - {nT}_{p}} \right)} \cdot {{\underset{\_}{v}}_{x^{\prime}{ax}}(t)} \cdot {\exp\left( {{- j}\;\omega_{x^{\prime}a}t} \right)}}{dt}}}}} & (54)\end{matrix}$

Equation (54) shows that shifting the receiver's time base relative tothe transmitter's by τ_(s) is equivalent to shifting the phase of thedetector complex output by exp(−jω₀τ_(s)) where ω₀ denotes the angularfrequency of the detector. Therefore, relative phase synchronizationbetween the different tone frequencies may be achieved by rotating thedetector's output phasors by an angle ω₀τ_(s). In some implementations,this may be more convenient than shifting the receiver's time base.

It shall be noted that some voltage components may be very weak or evennull. Depending on the sensor's rotation relative to the generator, itmay be impossible to determine the relative phasor, e.g., on thex-components as sensed by the x-sense coil 612.

In some implementations, the receiver uses diversity for determining therelative phasor by combining phasor products V _(x′bx)·V*_(x′ax), V_(x′by)·V*_(x′ay), and V _(x′bz)·V*_(x′az) of all components asreferring to the voltages induced into the x-, y- and z-sense coils 612,614, 616 respectively. Combining may be performed empirically just bysumming the phasor products. The relative phasor may then be obtained bynormalizing on the sum product as shown in Equation (55):

$\begin{matrix}{{\exp\left( {j} \right)} = \frac{{{\underset{\_}{V}}_{x^{\prime}{bx}} \cdot {\underset{\_}{V}}_{x^{\prime}{ax}}^{*}} + {{\underset{\_}{V}}_{x^{\prime}{by}} \cdot {\underset{\_}{V}}_{x^{\prime}{ay}}^{*}} + {{\underset{\_}{V}}_{x^{\prime}{bz}} \cdot {\underset{\_}{V}}_{x^{\prime}{az}}^{*}}}{{{{\underset{\_}{V}}_{x^{\prime}{bx}} \cdot {\underset{\_}{V}}_{x^{\prime}{ax}}^{*}} + {{\underset{\_}{V}}_{x^{\prime}{by}} \cdot {\underset{\_}{V}}_{x^{\prime}{ay}}^{*}} + {{\underset{\_}{V}}_{x^{\prime}{bz}} \cdot {\underset{\_}{V}}_{x^{\prime}{az}}^{*}}}}} & (55)\end{matrix}$

In other implementations, the receiver may employ a maximal ratiodiversity combining technique, e.g., by weighing components with anestimate of the SNR prior to combining. In yet other implementations,the receiver may employ selection diversity by selecting the productwith largest magnitude or with highest estimated SNR (quality).

To further improve synchronization accuracy or increase robustnessagainst noise and interference, estimation of the relative phasor may befurther enhanced by using averaging techniques over consecutivelydetected output phasors (time sequences). In some implementations, thereceiver may determine the relative phasor based on a moving average ofrelative phasors exp(j

_(n)) as obtained in consecutive time intervals. Other averagingtechniques based on time sequences exp(j

_(n)) may apply as well.

In a further step of post processing and as already disclosed above byequations (25)-(28), the receiver may rotate all detected phasorstowards the real axis by a common angle by multiplying all outputs witha phasor exp(j{circumflex over (φ)}_(n)) that may be an estimate ofexp(jω_(x′a)(T₀+(1−γ)nT_(p))). As already explained above, this phasorwill generally be slowly rotating as time advances (n increments).Having applied this rotation towards the real axis, the receiver mayselect the real part of all rectified outputs to finally get estimatesof all the components of the vectors {circumflex over (V)}_(x′a),{circumflex over (V)}_(x′b), {circumflex over (V)}_(y′), {circumflexover (V)}_(z′) as they may be required for determining a position.Selecting only the real part will remove the noise component on theimaginary part, hence generally improving a vector estimate and,finally, a position estimate.

Using (48) as an example, this operation of rotation and selection ofthe real part may be expressed by equation (56):{circumflex over (V)} _(x′bx) =Re{V _(x′bx)·exp(−j

)·exp(−j{circumflex over (φ)} _(n))}≅Re{V _(x′bx)·exp(−jω _(x′a)(T₀+(γ−1)nT _(p)))·exp(jω _(x′a)(T ₀+(γ−1)nT _(p)))}≅V _(x′bx)  (56)

The other x-components such as {circumflex over (V)}_(x′ax), {circumflexover (V)}_(y′x), and {circumflex over (V)}_(z′x) as well as all the y-and z-components may be obtained accordingly.

FIG. 20A to 20C further illustrate this process of relative phasesynchronization and rotation towards the real axis showing the complexplanes for each of the four detector outputs (x′ax, x′bx, y′x, andz′x-component). FIG. 20A, shows the complex phasors 2002, 2004, 2006,2008 of the four detector outputs (x′ax, x′bx, y′x, and z′x-component,respectively) prior to any synchronization. FIG. 20B shows the complexphasors 2012, 2014, 2016, 2018 after relative phase synchronization, andFIG. 20C shows the complex phasors 2022, 2024, 2026, 2028 after commonrotation towards the real axis.

A phasor estimate exp(j{circumflex over (φ)}_(n)) may be gained from atleast one of the received x-, y-, and z-components of at least one ofthe x′-, y′-, and z′-magnetic fields. Since the components may havedifferent polarities depending on the position and rotation of thesensor relative to the generator, the receiver may determineexp(j{circumflex over (φ)}_(n)) individually on components x′x, x′y,x′z, y′x, y′y, etc. and then eventually using a combining method assuggested above for determining the relative phasor exp (j

).

For improved performance and robustness, the phasor estimateexp(j{circumflex over (φ)}_(n)) may be determined based on consecutivenoisy detector outputs, e.g., by using a phase drift (frequency offset)estimator to compensate first for the phasor's rotation and then byusing averaging techniques as suggested above for determining therelative phasor exp(j

) as a second operation. Rotation compensation may be considered apost-detection fine frequency tuning of the receiver. Phase driftestimation, rotation compensation and averaging may be accomplished as amoving operation (e.g., a moving average). Alternatively, a linearregression method modified to a modulo 2π process may apply.

In some implementations, an enhanced receiver determines an estimateexp(j{circumflex over (φ)}_(n)) by using one of a diversity technique bycombining at least two components and additionally, by using sequencesof consecutively detected and relative phase corrected noisy phasors,e.g., to perform phase drift estimation, rotation compensation(frequency fine tuning) and averaging, or alternatively, linearregression on modulo 2π.

In case relative time drift between transmitter and receiver exceeded acertain tolerable limit, which may happen in practice, e.g., due to anextreme temperature drift which may manifest in a too fast rotation ofthe detector's output phasors, the receiver or the transmitter mayperform a coarse frequency correction. A too fast phase rotationindicates that the received tone signal is no longer centered in thefilter and, thus, may suffer from attenuation that could induce error inthe detected amplitude and eventually in the position estimate.

Therefore, in some implementations, the receiver may coarsely adjust thelocal oscillator frequencies of those synchronous detectors exhibitingnon-tolerable fast phasor rotation at their outputs so that the residualrotation is maintained below the tolerable limit. Alternatively, thereceiver may command the transmitter of concern via a datacommunications link to offset the magnetic field transmit frequencies bya certain amount.

For the purposes of diversity combining/selection and positioning, thereceiver may include functions to assess the quality of the receivedsignals in the various components. Quality may be assessed by estimatingthe SNR or by other signal integrity and consistency checks. A set ofsignals as used for magnetic vectoring may contain significantredundancy that can be used for quality assessment. The SNR of eachreceived signal component may be obtained from noise variance statisticsthat may fall out as side product when performing averaging over timesequences of detected phasors.

Interference of received tone signals by another magnetic vectoringtransmission (co-channel or adjacent channel interference) or byspurious emissions emanating from other sources (IPT systems,switched-mode power supplies, etc.) may therefore be detected by signalconsistency checks, e.g., if the amplitude and/or phase differencebetween signals v _(x′ax)(t) and v _(x′bx)(t) exceeded certainthresholds.

In some implementations, the receiver performs signal consistency checksas described above and estimates an SNR for each complex output of asynchronous detector.

FIG. 19 shows a block diagram of a portion of a magnetic fieldpositioning receiver 1900 using a bank of the synchronous detectors ofFIG. 18, in accordance with some implementations. The block diagramshows a bank of synchronous detectors 1902, e.g., as further detailed byFIG. 18, grouped into x-, y-, z-synchronous detector sub-banks, asindicated by the dotted boxes. Each sub-bank is associated to one of ananalog output v_(x)(t), v_(y)(t), and v_(z)(t) of a sense coil 612, 614,616. As described above, the respective signal generated by each of theplurality of sense coils 612, 614, 616 comprises at least a firstportion caused by the first alternating magnetic field oscillating at afirst f_(x′a) of the two frequencies f_(x′a), f_(x′b), a second portioncaused by the first alternating magnetic field oscillating at a secondf_(x′b) of the two frequencies f_(x′a), f_(x′b), and a third portioncaused by the second alternating magnetic field oscillating at the oneother frequency f_(y′). A processor is configured to estimate a relativephase angle Δφ between the first portion and the second portion. Forexample, FIG. 19 shows a phase synchronization unit 1904 as part of thepositioning receiver's post processing. The phase synchronization unit1904 has for inputs all complex (quadrature) outputs of the synchronousdetectors 1800. The phase synchronization unit 1904 produces for outputsthe phase corrected components of vectors {circumflex over (V)}_(x′),{circumflex over (V)}_(y′), {circumflex over (V)}_(z′) as they may berequired for determining a position in a position and direction findingunit (not shown in FIG. 19). The phase synchronization unit 1904determines an estimate of the relative phasor exp(j

) and establishes relative phase synchronization. Thus, in someimplementations, the processor (e.g., phase synchronization unit 1904)is configured to establish relative phase synchronization in the timedomain between the first portion, the second portion, and the thirdportion of the respective signal generated by each of the plurality ofsense coils 612, 614, 616 by shifting a detection time instant by anamount that is a function of the relative phase angle and a frequencyseparation between the one other frequency f_(y′) of the secondalternating magnetic field and at least one of the two frequenciesf_(xa′), f_(xb′) of the first alternating magnetic field. Similarly, theprocessor (e.g., the phase synchronization unit 1904) may be configuredto establish relative phase synchronization in the frequency domainbetween the first portion, the second portion, and the third portion ofthe respective signal generated by each of the plurality of sense coils612, 614, 616 by shifting a phase angle of at least one of the firstportion, the second portion and the third portion by an anglecorresponding to the relative phase angle Δφ or an integer multiple ofthe relative phase angle Δφ.

The phase synchronization unit 1904 further determines an estimate ofthe rotating phasor exp(j{circumflex over (φ)}_(n)), compensates for theresidual frequency offset (phase drift), and rotates all phasors by acommon angle, e.g., towards the real axis to finally get components ofvector estimates {circumflex over (V)}_(x′), {circumflex over (V)}_(y′),{circumflex over (V)}_(z′). Moreover, the phase synchronization unit1904 may assess quality of each component of vector estimates{circumflex over (V)}_(x′), {circumflex over (V)}_(y′), {circumflex over(V)}_(z′) and may separately deliver this information to the positionand direction finding unit (not shown in FIG. 19).

In a preferred implementation, the entire block as shown in FIG. 19 isimplemented in a digital signal processor and the input signalsv_(x)(t), v_(y)(t), and v_(z)(t) are (discrete-time) digital signals. Inanother implementation, the positioning receiver implements multipleblocks as shown in FIG. 19, which can be instantiated and assigned toreceive and process magnetic vectoring signals emanating from differenttransmitters transmitting at different frequencies (in differentbeaconing channels). In yet another implementation,Fast-Fourier-Transform (FFT) techniques or similar algorithms are usedto implement the banks of synchronous detectors and to reducecomputational complexity (burden) of the digital signal processor.

FIG. 21 illustrates a block diagram of an analog front end (AFE) 2100 ofa 3-axis magnetic field positioning receiver, in accordance with someimplementations.

The AFE 2100 may provide the digital signals v_(x)(t), v_(y)(t), andv_(z)(t) at its three outputs that may represent the three input signalsof the synchronous detector sub-banks as shown in FIG. 19. Each of thethree AFE channels comprises an input protector (limiter) 2102, apreamplifier 2104, a filter 2106, a variable gain amplifier 2108, andoptionally an analog-to-digital (A/D) converter 2110.

The input protector 2102 serves to protect the preamplifier 2104 frombeing damaged when the magnetic field sensor (e.g., the sense coils 612,614, 616) is exposed to a strong magnetic field, e.g., during activepower transfer from an IPT system. The input protector 2102 limits theinput voltage and is designed in a manner such that there is nosubstantial current flow when the circuit is limiting so that there isno substantial power loss and no heating effects. The preamplifier 2104may have a gain (e.g., 20 dB) and a high impedance input (>100 kΩ) and arelatively low output impedance (e.g., <50 Ohm) for driving thefollowing filter 2106.

The filter 2106 may be a bandpass filter having a passband withreasonably low ripple and sufficient width to cover the full frequencyband as it may be specified for magnetic vectoring and having sufficientsuppression (e.g., >60 dB) of signals received out-of-band, particularlyat IPT operating frequencies, e.g., 85 kHz. The filter 2106 may also actas anti-aliasing filter as needed for sampling the signal in the A/Dconverter 2110.

The variable gain amplifier 2108 ensures that the A/D converter 2110always operates in the favorable range over the large dynamic range andcompensates for large receive signal level variations as they may occurin real scenarios, due to the so-called “near-far” effect. The variablegain amplifier 2108 may be controlled by the digital processing unitthat follows the AFE 2100 providing an automatic gain control function(not shown in FIG. 21).

In some implementations, at least three co-planar sense coils may beconfigured to provide at least a two-axis sensor in combination. In yetother implementations, four co-planar sense coils may be configured toprovide a three-axis sensor in combination and may be suitably disposedon a ferrite substrate may be used to sense the three alternatingmagnetic fields as needed for magnetic vectoring. Such a 4-coilarrangement may act as a 3-axis sensor. For a 4-coil sensor, the AFE2100 of FIG. 21 may be extended to a 4-channel AFE having four analoginputs and four digital outputs. The required linear combinationsproviding the three signals v_(x)(t), v_(y)(t), and v_(z)(t) may then beperformed in the digital domain in a block prior to synchronousdetection, as previously described in connection with FIG. 19.

FIG. 22 illustrates an orthogonal coil arrangement 2200 for a 3-axisgenerator or sensor, in accordance with some implementations. It usesthree orthogonal generator coils 602, 604, 606. Typically, the coils602, 604, 606 may have a few turns of relatively thin copper wire with across section of <0.2 mm². The x′- and y′-coils 602, 604, respectively,are wound around a ferrite structure 2202. The z′-coil 606 may be arectangular coil disposed along the contours near the edges of theferrite structure 2202. Alternatively, the z′-coil 606 may be woundaround the long perimeter entirely at the edges of the ferrite structure2202. In a preferred implementation, the ferrite structure 2202 isshared by the IPT and MV systems. This allows for a large volume of theferrite structure 2202 to capture larger amounts of magnetic flux and,thus, provide a more accurate indication of the alignment between thegenerator and sensor.

In some other implementations, the 3-coil arrangement of FIG. 22 appliesto a 3-axis sensor. In such implementations, the axis designation x′, y′and z′ would change to x, y and z, respectively. A 2-axis generator forvehicle positioning applications generating an x′- and y′-magneticmoment may be achieved by omitting the z′-coil 606 shown in FIG. 22 orby driving the z′-coil with a substantially zero-current.

In other implementations, a multi-axis generator or sensor uses acombination of at least one IPT coil and at least one magnetic vectoringcoil. In some implementations, the x′-coil 602 is formed by reusing theIPT coil, e.g., a “Double-D” coil, a “Solenoid”-coil, a “Bi-polar”-coil,and the y′-coil 604 is a supplementary dedicated magnetic vectoringcoil.

FIG. 23 illustrates a frequency division 4-tone magnetic fieldtransmission scheme 2300, in accordance with some implementations. Afirst variant applies to a 3-axis generator where a double-tone withfrequencies f_(x′a), and f_(x′b) is used to excite the x′-coil 602 andsingle tones with frequencies f_(y′) and f_(z′) for the y′-coil andz′-coils, respectively. Adjacent tones are separated by Δf (tonefrequency spacing). The second variant applies to a 2-axis generatorwhere a double-tone (f_(x′a), f_(x′b)) and a double-tone (f_(y′a),f_(y′b)) is used to excite each the x′-coil 602 and y′-coil 604,respectively. The second double-tone transmitted via the y′-coil 604 maybe not necessary for the basic function but may improve robustness ofthe system as it provides more redundancy for determination of thesynchronization. As previously mentioned, any redundancy in thetransmitted signals may be used for enhanced signal consistency andintegrity checks. But even more important, the system may establishrelative phase synchronization and determine a position even if one ofthe four tones is jammed by a narrow-band interference signal.

Furthermore, FIG. 23 shows a 4-tone transmission in each of the twoadjacent magnetic beaconing channels (e.g., channel n and channel n+1).Adjacent tones of two different channels may be separated by Δƒ_(grd)>Δfproviding a guard band between adjacent channels for purposes as alreadyexplained above.

In another aspect of the disclosure, the channel number n that aparticular positioning transmitter is assigned to may implicitly serveas an identifier so that no transmitting of an explicit ID is needed.Assuming out-of-band data communications in parallel (e.g., via UHFWLAN) as well as a central coordinator, ID's may be communicatedout-of-band and the central coordinator may inform the positioningreceiver that transmissions on channel n belong to the transmittermatching the communicated ID.

In a further aspect of the disclosure, it may be desirable to minimizethe peak-to-average ratio (crest factor) of the multi-tone transmissionscheme. It shall be noted that the sum signal of a multi-tonetransmissions may exhibit a high peak-to-average level ratio if thereexist time instances where all tones have the same phase thus adding upconstructively. A high crest factor may be disadvantageous, e.g., in asystem where transmit levels are constrained by regulatory limits basedon peak detection, e.g., ICNIRP EMF exposure limits. In a transmissionscheme using more than two tones, the crest factor may be minimized byoffsetting the phase of at least one second tone relative to the phaseof a first tone whose phase is maintained. Applied to the exemplarymulti-tone transmission scheme as given by equations (19)-(21),rewritten here,i _(x′)(t)=I _(x′a) sin(ω_(x′a) t)+I _(x′b) sin(ω_(x′b) t)  (19)i _(y′)(t)=I _(y′) sin(ω_(y′) t+φ _(y′)),  (20)i _(z′)(t)=I _(z′) sin(ω_(z′) t+φ _(z′)).  (21)the crest factor may be minimized by optimizing phase offsets φ_(y′) andφ_(z′). Since phase offsets may remain fixed during transmission and maybe known to the receiver, these phase offsets can be taken into accountin the process of synchronization.

In some implementations, the multi-tone transmission is optimized withrespect to the crest factor by offsetting the phase of at least onesecond tone relative to the phase of a first tone whose phase ismaintained. In yet other implementations, relative phase information asneeded for relative polarity ambiguity resolution is provided to thereceiver by using a dedicated synchronization signal. Thissynchronization signal may be a synchronization sequence that ismodulated on at least one of the tone signals. This synchronizationsequence may be a pseudo-random sequence such as a “m”-sequence, aGold-sequence, etc. characterized by adequate auto and/orcross-correlation properties as needed to reliably synchronize thereceiver with the required accuracy, taking the modulation (symbol,data) rate into account. At least one of an amplitude and phasemodulation may apply. The modulation signal may be adequately filteredin regards to an efficient use of the available spectrum and minimumadjacent channel interference. The synchronization sequence may betransmitted periodically, e.g., at least every T_(p) second or integermultiples thereof, where T_(p) defines the position update period asintroduced above.

The synchronization sequence may also serve as an ID since it may beneeded in some system implementations to identify a transmitter. In suchimplementations, the transmitter would use one of a predefined set ofdifferent synchronization sequences, e.g., a set of Gold-sequences.Without a priori knowledge, the receiver may first demodulate thereceived signal to identify the synchronization sequence of a particulartransmission and then use that sequence as the local replica forcorrelating the received signal in order to find the synchronizationtime instance.

Such an exemplary transmission format is shown in FIG. 24. FIG. 24illustrates a modulation waveform of a transmission frame 2402comprising a synchronization sequence 2400 and a multi-tonetransmission, in accordance with some implementations. The transmissionframe 2402 may have the duration T_(p) or multiples thereof and issubdivided into a synchronization sequence interval 2404 and amulti-tone frequency interval 2406. The synchronization sequence 2400 isindicated by the exemplary binary data sequence {1, 1, 0, 1, 0, 0, 0, 1,0, 0, 1, 1, 0} that is modulated using a filtered (pulse-shaped)“return-to-zero” antipodal modulation scheme. For example, a “1” may beindicated by a spike or impulse rising above and then settling back tozero magnitude, while a “0” may be indicated by a spike or impulsefalling below and then settling back to the zero magnitude. Themodulation rate is equal to the frequency spacing Δf of the multi-tonetransmission. The resulting modulated synchronization signal may providethe correlation properties as required to synchronize the receiver withan accuracy within a small fraction of 1/Δƒ. Thus, in someimplementations the processor (e.g., the phase synchronization unit1904) may be configured to establish relative phase synchronizationbetween the first portion, the second portion, and the third portion ofthe respective signal generated by each of the plurality of sense coils612, 614, 616 by using the synchronization sequence 2400 that istransmitted in at least one of the first alternating magnetic field(e.g., by the generator coil 602) or the second alternating magneticfield (e.g., by the generator coil 604).

With respect to the TDM implementations previously described inconnection with FIGS. 7B and 7C, pulse modulated single-carrier signals(e.g., common carrier frequency wave pulses) may be transmitted in everytime slot as exemplarily shown in FIG. 25. The pulse shape may be theresult of a design trade-off between spectral efficiency and averagetransmit power, e.g., under a transmitter peak power constraint. In someother implementations, additional guard intervals are inserted betweenwave pulses (not shown in FIG. 25) to guarantee that no inter-slotinterference occurs, e.g., due to time synchronization errors as furtherexplained below.

As previously shown for the 3 or 2-axis generator/3-axis sensor system,the position finding problem of vehicle charging only requires knowledgeof the relative polarities of the detected voltage vectors. In a pulsemodulated single-carrier TDM system, relative polarity means relativephase between the signal components as sensed in the different timeslots with the different sensors. To correctly detect signal magnitudeand polarity of the x′-, y′- and z′-magnetic field signal, the timing ofthe magnetic positioning receiver is adjusted to the time slots (e.g.,the time slots 782 a, 784 a, 786 a, 788 a of FIG. 7C) as defined by thesequence of the transmitted wave pulses 2502, 2504, 2506, 2508. Thistime slot synchronization will ensure that there is no substantialinter-slot interference falsifying magnitude and polarity as detected bythe magnetic positioning receiver.

In some implementations all wave pulses except the start of frame wavepulse 2502 in time slot t_(x′a) are transmitted with equal phase, e.g.,0°. In some implementations, the start of frame wave pulse 2502 istransmitted with a 90° phase shift relative to the phases of the otherwave pulses 2504, 2506, 2508 so that time slot t_(x′a) (e.g., the timeslot 782 a) may be distinguishable from the other time slots (e.g., thetime slots 784 a, 786 a, 788 a) in all circumstances, e.g., if the phase(polarity) of one or more wave pulses is altered by the transmissionchannel as determined by the relative position and rotation of thegenerator and sensor frame. Accordingly, the first wave pulse 2502 has apredetermined phase shift (e.g., 90 degrees) with respect to eachfollowing wave pulse 2504, 2506, 2508 of the plurality of wave pulses.In general, magnitude and phase (polarity) of the x′-, y′- andz′-magnetic field signals as transmitted in the different time slots maychange as exemplarily shown in FIG. 26, which illustrates each of thewave pulses 2502, 2504, 2506, 2508.

The set of coil excitation currents that generate the magnetic fieldbeacon signals as transmitted in the different time slots and as shownin FIG. 25 may be mathematically described as follows:i _(x′a)(t)=I _(x′a) p(t−t _(x′a))sin(ω₀ t+π/2),  (22)i _(x′b)(t)=I _(x′b) p(t−t _(x′b))sin(ω₀ t),  (23)i _(y′)(t)=I _(y′) p(t−t _(y′))sin(ω₀ t),  (24)i _(z′)(t)=I _(z′) p(t−t _(z′))sin(ω₀ t),  (25)where I_(x′a) denotes the peak amplitude of the coil current i_(x′a)(t),p(t−t_(x′a)) denotes the pulse envelope function positioned in time slott_(x′a), and ω₀ denotes the carrier angular frequency. Denotations forthe quantities defining the other signals x′b, y′, and z′ are shownaccording to (26)-(28). Defining time slot duration T_(s), pulsepositions may be expressed as:t _(x′b) =t _(x′a) +T _(s),  (26)t _(y′) =t _(x′a)+2T _(s),  (27)t _(z′) =t _(x′a)+3T _(s),  (28)

In some implementations, however not necessary for the basic methoddisclosed herein, time slot duration T_(s) is an integer multiple k ofthe carrier wave period, which may be expressed as:

$\begin{matrix}{{T_{s} = {k\frac{2\pi}{\omega_{0}}}},{k \in {\mathbb{N}}},} & (29)\end{matrix}$

In another implementation, a frame comprises only three time slots(e.g., 712 a, 714 a, 716 a) in accordance with FIG. 7B and one wavepulse of a frame, e.g., wave pulse i_(x′)(t) is transmitted with a 90°phase shift relative to the phase of the other two wave pulses to mark aspecific time slot, e.g., time slot t_(x′) and so that this time slotmay be distinguishable from the other time slots in all circumstances,e.g., if the phase (polarity) of one or more wave pulses is altered bythe transmission channel as determined by the relative position androtation of the generator and sensor frame.

In a system in accordance with some implementations, the magnetic fieldpositioning receiver uses a plurality of detectors to filter and detecteach of the voltage signal components as received by each sense coil ineach time slot. FIG. 27 shows a block diagram of an exemplarysynchronous detector 2700 that may be used to optimally filter anddetect the wave pulses 2502, 2504, 2506, 2508 as transmitted at angularfrequency ω₀ and received by any of the sense coils 612, 614, 616 intime slot n, where n denotes the time slot counter. In time slot n, thesynchronous detector 2700, if correctly timed, provides at its twooutputs the real and imaginary part (I- and Q-component), respectively,of a complex value that may represent the complex voltageV(n)=Re{V(n)}+jIm{V(n)} of the signal as received by a particular sensecoil. V(n) is also called a phasor in the following.

Using complex signal representation and assuming perfect carrierfrequency synchronization, the operation of the synchronous detector2700 as shown in FIG. 27 may be expressed as:

$\begin{matrix}{{\underset{\_}{V}(n)} = {\int_{{nT}_{s} - T_{s/2} + \tau_{s}}^{{nT}_{s} + T_{s/2} + \tau_{s}}{{w\left( {t - {nT}_{s} - \tau_{s}} \right)}{{v(t)} \cdot {\exp\left( {{- j}\;\omega_{0}t} \right)}}{dt}}}} & (30)\end{matrix}$where w(·) is a windowing function, v(t) the input voltage signal asreceived from one of the sensor outputs, e.g., from the x-sensor output(v_(x)(t)), and τ_(s) a time offset parameter used to adjust timing ofthe synchronous detector 2700 as part of a time slot synchronizationprocess.

In some implementations, the windowing function is matched to thetransmit pulse so as to maximize signal-to-noise ratio (SNR) in outputsV(n). In other implementations, the windowing function is optimized forother criteria, e.g., carrier frequency offset tolerance, adjacentchannel suppression, etc.

FIG. 28 shows a block diagram of a portion of a TDM magnetic field3-branch receiver 2800 for a 3-axis sensor system, in accordance withsome implementations. The block diagram shows the 3-branch receiver 2800using three synchronous detectors 2700 a, 2700 b, 2700 c (see FIG. 27).Each synchronous detector 2700 a-2700 c (branch) is associated to one ofan analogue output of a sense coil 612, 614, 616 as further detailedbelow. Moreover, FIG. 28 shows a post processing unit 2802 that performsat least frame synchronization, time slot synchronization, phasorrotation, and demultiplexing (serial to parallel conversion) of thesequentially received phasors in each receiver branch. The postprocessing unit 2802 provides at least three complex (quadrature) inputsV _(x)(n), V _(y)(n), and V _(z)(n), nine scalar outputs, which are thecomponents of the vectors {circumflex over (V)}_(x′), {circumflex over(V)}_(y′), {circumflex over (V)}_(z′) as they may be required fordetermining a position in a position and direction finding unit (notshown in FIG. 28).

In some implementations, the post processing unit 2802 detects thesynchronization signals as received, e.g., in time slots t_(x′a) in allreceiver branches assuming a TDM scheme in accordance with FIG. 7C. Thepost processing unit 2802 establishes frame synchronization, which isrequired for correct demultiplexing of signals received in consecutivetime slots. It also performs time slot synchronization by determining atime offset and by adjusting a common timing parameter τ_(s) of thedetectors to match the transmitter's time slots.

In some implementations, the post processing unit 2802 uses thesynchronization signal as received (e.g., in time slots t_(x′a)),assuming a TDM scheme in accordance with FIG. 7C, and at least onesignal received in another time slot to estimate the timing offset andto establish time slot synchronization.

In some implementations, equation (29) holds and the receiver preciselyknows time slot duration T_(s). Moreover, transmit-side and receive-sidetime and frequency bases are sufficiently accurate, so thatconsecutively detected phasors V(n) in a receiver branch aresubstantially equally oriented (but generally not equally directed) overa considerable number of time slots. Under certain conditions, this mayalso apply to phasors concurrently detected in other receiver branches,so that all detected phasors exhibit substantially equal orientation,but generally not equal sense.

Therefore, in some implementations in accordance with equations (22) to(25), the post processing unit 2802 estimates a phasor angle {circumflexover (φ)} based on the phasors detected during time slots t_(x′a) andt_(x′b) and in all receiver branches and rotates all phasors detected intime slots t_(x′b), t_(y′), and t_(z′) by an angle −

towards the real axis and selects the real part to finally providevector estimates {circumflex over (V)}_(x′), {circumflex over (V)}_(y′),{circumflex over (V)}_(z′) at its outputs. This process of phasorrotation may also be considered as using the phasors detected in timeslots t_(x′a) and t_(x′b) as phase reference for detecting the phasorsreceived in time slots t_(y′), and t_(z′). This is consistent with apositioning approach that requires relative phase (polarity) informationonly.

In some other implementations, phasor angle {circumflex over (φ)} isestimated by means of all phasors as detected in all time slots and inall receiver branches, e.g., using a joint relative polarity detectionand phase estimation approach.

In some other implementations, transmit-side and receive-side time andfrequency bases may not be accurate enough so that substantial rotationresults in consecutively detected phasors. In such implementations, thepost processing unit 2802 may additionally perform carrier frequencysynchronization by estimating and correcting the carrier frequencyoffset. Frequency offset correction may be performed by de-rotatingdetected phasors, by adjusting the frequency of the synchronousdetectors (ω₀), or by sending frequency control commands to the magneticfield positioning transmitter to adjust the transmit carrier frequency.

In some implementations, the post processing unit 2802 additionallycombines outputs detected in time slots t_(x′a) and t_(x′b) to fullyutilize available signal energy and to produce a vector estimate{circumflex over (V)}_(x′) with improved signal-to-noise ratio. Assumingtransmit signal definitions (22) and (23), combining may be accomplishedby rotating the phasor detected in time slot t_(x′a) by 90° and byadding it constructively to the phasor detected in time slot t_(x′b),and by scaling the sum by a factor of 0.5. The combined phasor will haveabout equal magnitude as the individual phasors but less noise onaverage. This operation may apply to phasors detected in every receiverbranch.

FIGS. 29A and 29B further illustrate the process of phasor rotationtowards the real axis, phasor combination, and real part selection inthe complex planes for the case of a perfect time and carrier frequencysynchronization and in the absence of noise. FIG. 29A shows the sequenceof phasors 2902, 2904, 2906, 2908 as detected in consecutive time slotst_(x′a), t_(x′b), t_(y′), and t_(z′) in the x-branch of the 3-branchreceiver 2800. FIG. 29B shows the three relevant phasors 2910, 2912,2914 after common rotation towards the real axis. The dashed arrow shallindicate that the relative polarities (senses) of phasors detected intime slot t_(y′), and t_(z′) may generally differ depending on theposition and rotation of the generator frame relative to the sensorframe.

In yet other implementations, this application also contemplates acode-division multiplexing scheme (CDM) to generate magnetic fieldbeacon signals with magnetic moments in different axis directions. Asopposed to time-division multiplexing (TDM), magnetic field beaconsignals are transmitted concurrently (in the same time interval) usingdifferent spreading codes. Thus, the alternating magnetic fieldgenerated by the generator coils 602, 604, 606 as well as the voltageinduced in the sense coils 612, 614, 616 by that alternating magneticfield comprises at least a first portion caused by a first beacon signalof the plurality of beacon signals, a second portion caused by a secondbeacon signal of the plurality of beacon signals, and a third portioncaused by a third beacon signal of the plurality of beacon signals. Insome implementations, orthogonal spreading codes as known in the art areused to differentiate the x′-, y′-, and z′-magnetic field beacon signalsin the receiver. To preserve orthogonality, these codes signals may haveto be transmitted synchronously (e.g., without time offset). Other setsof spreading codes, e.g., codes with non-zero but low cross-correlationfor any time offset may be used to separate magnetic field beaconsignals emanating from different sources in the receiver, e.g., signalsemanating from different charging bases or vehicles, depending on thedirection of transmission. These code signals may be transmittedasynchronously in random time epochs.

In some implementations, the length of the spreading codes as used forcode-division multiplexing of magnetic field beacon signals of the samesource (e.g. the length of the orthogonal codes) corresponds to theposition data update period of the magnetic field positioning system,e.g., 200 ms (5 position updates per second).

The magnetic positioning receiver uses local replicas of transmittedspreading code signals for detecting the received signals bycorrelation, once the receiver is in synchronism with received codesignals.

In a 3-axis generator system in accordance with some implementations,spreading codes are modulated onto a sinusoidal carrier signal. In thiscase, the set of coil excitation currents that generate the magneticfield beacon signals as concurrently transmitted with different codesequences may be mathematically described as follows:i _(x′)(t)=Re{I _(x′) c _(x′)(t)exp(jω ₀ t)},  (31)i _(y′)(t)=Re{I _(y′) c _(y′)(t)exp(jω ₀ t)},  (32)i _(z′)(t)=Re{I _(z′) c _(z′)(t)exp(jω ₀ t)},  (33)where I_(x′) denotes the peak amplitude of the coil current i_(x′)(t), c_(x′)(t) the complex envelope as resulting from the spreading codemodulation and some filtering for purposes of spectral shaping.Denotations for the quantities defining the other signals, y′, and z′are accordingly.

In some implementations, the magnetic field positioning transmitteradditionally applies a pre-emphasis on the transmit signals tocompensate for the frequency response of the transmission channel, whichmay show a linear increase with frequency as the voltage induced into asense coil linearly increases with frequency. Pre-emphasis may beparticularly useful if the fractional bandwidth of the spectralspreading is high.

The magnetic field positioning receiver may use a plurality ofcorrelation detectors for filtering and detecting each of the voltagesignal components as received by each sense coil 612, 614, 616 andtransmitted using different spreading codes. FIG. 30 shows a blockdiagram of an exemplary correlation detector 3000 for detecting thesignal v(t) as it may be received, e.g., via the x-sense coil 612. Ituses the conjugate complex of the transmit waveforms as local replicas.The correlation detector 3000 comprises a quadrature mixer fordown-conversion and de-spreading and first and second integrators 3006,3008, respectively. The quadrature mixer comprises a first mixer 3002configured to multiply the input signal by the real part of the complexlocal replica to provide the I-component, and a second mixer 3004configured to multiply the input signal by the imaginary part of thecomplex local replica to provide the Q-component. The outputs of thefirst and second mixers 3002, 3004 are input to the first and secondintegrators 3006, 3008, respectively. Both integrators 3006, 3008perform the same function as a FIR low pass filter by weighing thebaseband signal at the filter impulse response (window function).Integration may be performed over a time period T_(p) corresponding withthe position update period or any fraction thereof. In someimplementations T_(p) may correspond with the repetition period of acode sequence, e.g., a set of orthogonal code sequences. The correlationdetector 3000, if code synchronous, outputs complex values (phasors)that may represent the complex voltage V(n)=Re{V(n)}+jIm{V(n)} of thesignal received by a sense coil, where n is the detection time intervalcounter.

FIG. 31 shows a block diagram of a portion of a CDM magnetic fieldpositioning 3-branch receiver 3100 for a 3-axis sensor system, inaccordance with some implementations. The block diagram shows a 3-branchreceiver 3100 using a bank 3104 of correlation detectors 3000 (see FIG.30), grouped into x-, y-, z-detector sub-banks (branches), as indicatedby the dotted boxes. Each sub-bank (branch) is associated to one of ananalog output (v_(x)(t), v_(y)(t), v_(z)(t)) of a sense coil 612, 614,616. FIG. 31 shows a post-processing unit 3102 that performs at leastcode synchronization and phasor rotation of the sequentially receivedphasors in each receiver branch. The post-processing unit 3102 has forinputs all complex (quadrature) outputs of the correlation detectors.The post-processing unit produces for outputs the phase correctedcomponents of vectors {circumflex over (V)}_(x′), {circumflex over(V)}_(y′), {circumflex over (V)}_(z′) as they may be utilized fordetermining a position in a position and direction finding unit (notshown in FIG. 31).

In some implementations, the post processing unit 3102 establishes codesynchronization with all CDM signals as received in all receiverbranches and performs code synchronization tracking by determining atime offset and by adjusting a common timing parameter τ_(s) of thecorrelation detectors 3000 to match the transmitted code sequences.

In some implementations, transmit-side and receive-side time andfrequency bases are sufficiently accurate, so that consecutivelydetected phasors V(n) in all receiver branches are substantially equallyoriented (but generally not equally directed) over a considerable numberof time slots. Therefore, in some implementations in accordance withequations (31) to (33), the post processing unit estimates a phasorangle {circumflex over (φ)} based on the phasors detected, e.g., basedon all receive signal components of the x′-magnetic field as transmittedwith spreading code modulation c _(x′)(t) and as sensed by all sensecoils 612, 614, 616. The post processing unit 3102 rotates all phasorsdetected by all correlation detectors 3000 in all receiver branches byan angle −

towards the real axis and selects the real part to finally providevector estimates {circumflex over (V)}_(x′), {circumflex over (V)}_(y′),{circumflex over (V)}_(z′) at its outputs. This process of phasorrotation may be also considered as using detected phasors of signalstransmitted with spreading code modulation c _(x′)(t) as phase referencefor detecting the phasors of signals transmitted with spreading codemodulation c _(y′)(t) and c _(z′)(t). This is consistent with apositioning approach that requires relative phase (polarity) informationonly.

In some other implementations, an estimate of phasor angle {circumflexover (φ)} is determined by means of all detected phasors of all signalsas transmitted with the different spreading codes and received in allreceiver branches, e.g., using a joint relative polarity detection andphase estimation approach.

In some other implementations, transmit-side and receive-side time andfrequency bases may not be accurate enough so that substantial rotationresults in consecutively detected phasors. In such implementations, thepost processing unit 3102 may additionally perform carrier frequencysynchronization by estimating and correcting the carrier frequencyoffset. Frequency offset correction may be performed by de-rotatingdetected phasors, by adjusting the frequency of the synchronousdetectors (ω₀), or by sending frequency control commands to the magneticfield positioning transmitter to adjust transmit carrier frequency.

FIGS. 32A and 32B further illustrate the process of phasor rotationtowards the real axis and real part selection in the complex planes forthe case of a perfect time and carrier frequency synchronization and inthe absence of noise. FIG. 32A shows the phasors 3202, 3204, 3206 asdetected on the different code signals c_(x′), c_(y′), and c_(z′) in thex-branch of the 3-branch receiver 3100. FIG. 32B shows the phasors 3210,3212, 3214 after common rotation towards the real axis. The dashed arrowshall indicate that the relative polarities (senses) of phasors asdetected on code signals c_(y′), and c_(z′) may generally differdepending on the position and rotation of the generator frame relativeto the sensor frame.

The above methods and systems described for a 3-axis generator/3-axissensor system, if modified accordingly, may also apply to a 2-axisgenerator/3-axis sensor or to a 3-axis generator/2-axis sensor system orto any other system transmitting at least two different magnetic fields.

FIG. 33 is a flowchart 3300 depicting a method for determining arelative position of a wireless power transmitter from a wireless powerreceiver, in accordance with some implementations. Flowchart 3300corresponds to the TDM method previously described with reference to atleast FIGS. 4-32 and may correspond to a magnetic vectoring fieldsensor. Although the flowchart 3300 is described herein with referenceto a particular order, in various implementations, blocks herein may beperformed in a different order, or omitted, and additional blocks may beadded.

Block 3302 includes generating, by each of a plurality of sense coils, arespective voltage signal under influence of an alternating magneticfield comprising a plurality of wave pulses, each wave pulse occurringin a respective time slot of a plurality of time slots. For example, aspreviously described in connection with at least FIG. 6, a plurality ofsense coils 612, 614, 616, may each be configured to generate arespective voltage signal under influence of an alternating magneticfield comprising a plurality of wave pulses (e.g., a first wave pulse2502, a second wave pulse 2504, a third wave pulse 2506, and a fourthwave pulse 2508) (see FIGS. 25-29B), each wave pulse occurring in arespective time slot 782 a, 784 a, 786 a (see FIG. 7C) of a plurality oftime slots).

Block 3304 includes determining the relative position of the wirelesspower transmitter from the wireless power receiver based on therespective voltage signal from each of the plurality of sense coils. Forexample, as previously described in connection with at least FIGS. 4-32a processor or controller downstream from and/or including the postprocessing unit 2802 (see FIG. 28) may be configured to determine therelative position of the wireless power transmitter from the wirelesspower receiver based on the respective voltage signal from each of theplurality of sense coils.

FIG. 34 is a flowchart 3400 depicting a method for determining arelative position of a wireless power transmitter from a wireless powerreceiver, in accordance with some implementations. Flowchart 3400corresponds to the TDM methods previously described. The flowchart 3400is described herein with reference to at least FIGS. 4-32 and maycorrespond to a magnetic vectoring field generator. Although theflowchart 3400 is described herein with reference to a particular order,in various implementations, blocks herein may be performed in adifferent order, or omitted, and additional blocks may be added.

Block 3402 includes generating at least a first signal, a second signaland a third signal, each comprising one of at least one respective wavepulse of a plurality of wave pulses, each wave pulse occurring in arespective time slot of a plurality of time slots. For example, aspreviously described in connection with at least FIG. 6, a drivercircuit may generate a first signal, a second signal and a third signal,each comprising one of at least one respective wave pulse of a pluralityof wave pulses 2502, 2504, 2506, 2508 (see FIGS. 25-29B), each wavepulse occurring in a respective time slot 782 a, 784 a, 786 a (see FIG.7C) of a plurality of time slots.

Block 3404 includes generating an alternating magnetic field by drivingeach coil of a plurality of coils with a respective one of the firstsignal, the second signal and the third signal. For example, aspreviously described in connection with at least FIG. 6 the alternatingmagnetic field may be generated by driving the coil 602 with the firstsignal (e.g., the wave pulses 2502 and 2504), driving the coil 604 withthe second signal (e.g., the wave pulse 2506), and driving the coil 606with the third signal (e.g., the wave pulse 2508). Where the coils 602,604, 606 are driven with the wave pulses 2502, 2504, 2506, 2508, thewave pulses 2502 and 2504 may occur in a first time slot (e.g., timeslot 782 a of FIG. 7C), the wave pulse 2506 may occur in a second timeslot (e.g., time slot 784 a of FIG. 7C) and the wave pulse 2508 mayoccur in a third time slot (e.g., time slot 786 a of FIG. 7C). Thus,each of the coils 602, 604, 606 may contribute to generating thealternating magnetic field during their respective time slots.

FIG. 35 is a flowchart 3500 depicting a method for determining arelative position of a wireless power transmitter from a wireless powerreceiver, in accordance with some implementations. Flowchart 3500corresponds to the CDM method previously described with reference to atleast FIGS. 4-32 and may correspond to a magnetic vectoring fieldsensor. Although the flowchart 3500 is described herein with referenceto a particular order, in various implementations, blocks herein may beperformed in a different order, or omitted, and additional blocks may beadded.

Block 3502 includes generating, by each of a plurality of sense coils, arespective voltage signal under influence of an alternating magneticfield comprising a plurality of beacon signals occurring simultaneously,each beacon signal modulated with a unique spreading code. For example,as previously described in connection with at least FIG. 6, a pluralityof sense coils 612, 614, 616, may each be configured to generate arespective voltage signal under influence of an alternating magneticfield comprising a plurality of beacon signals occurring simultaneously,each beacon signal modulated with a unique spreading code (e.g.,c_(x′)(t), c_(y′)(t), c_(z′)(t)) (see FIGS. 30-32B).

Block 3504 includes determining the relative position of the wirelesspower transmitter from the wireless power receiver based on therespective voltage signal from each of the plurality of sense coils. Forexample, as previously described in connection with at least FIGS. 4-32a processor or controller downstream from and/or including the postprocessing unit 3102 (see FIG. 31) may be configured to determine therelative position of the wireless power transmitter from the wirelesspower receiver based on the respective voltage signal from each of theplurality of sense coils.

FIG. 36 is a flowchart 3600 depicting a method for determining arelative position of a wireless power transmitter from a wireless powerreceiver, in accordance with some implementations. Flowchart 3600corresponds to the CDM method previously described. The flowchart 3600is described herein with reference to at least FIGS. 4-32 and maycorrespond to a magnetic vectoring field generator. Although theflowchart 3600 is described herein with reference to a particular order,in various implementations, blocks herein may be performed in adifferent order, or omitted, and additional blocks may be added.

Block 3602 includes generating at least a first signal, a second signaland a third signal, each comprising a respective beacon signal of aplurality of beacon signals occurring simultaneously, each beacon signalmodulated with a unique spreading code. For example, as previouslydescribed in connection with at least FIG. 6, a driver circuit maygenerate a first signal, a second signal and a third signal, eachcomprising a respective beacon signal of a plurality of beacon signalsoccurring simultaneously, each beacon signal modulated with a uniquespreading code (e.g., c_(x′)(t), c_(y′)(t), c_(z′)(t) (see FIGS.30-32B).

Block 3604 includes generating an alternating magnetic field by drivingeach coil of a plurality of coils with a respective one of the firstsignal, the second signal and the third signal. For example, aspreviously described in connection with at least FIG. 6 the alternatingmagnetic field may be generated by driving the coil 602 with the firstsignal (e.g., the beacon signal modulated with the spreading codec_(x′)(t)), driving the coil 604 with the second signal (e.g., thebeacon signal modulated with the spreading code c_(y′)(t)), and drivingthe coil 606 with the third signal (e.g., the beacon signal modulatedwith the spreading code c_(z′)(t)). Where the coils 602, 604, 606 aredriven with the respective beacon signals, each modulated with one ofthe unique spreading codes c_(x′)(t), c_(y′)(t), and c_(z′)(t), allbeacon signals may be transmitted simultaneously.

The various operations of methods described above may be performed byany suitable means capable of performing the operations, such as varioushardware and/or software component(s), circuits, and/or module(s).Generally, any operations illustrated in the FIG.s may be performed bycorresponding functional means capable of performing the operations.

Information and signals may be represented using any of a variety ofdifferent technologies and techniques. For example, data, instructions,commands, information, signals, bits, symbols, and chips that may bereferenced throughout the above description may be represented byvoltages, currents, electromagnetic waves, magnetic fields or particles,optical fields or particles, or any combination thereof.

The various illustrative logical blocks, modules, circuits, andalgorithm steps described in connection with the implementationsdisclosed herein may be implemented as electronic hardware, computersoftware, or combinations of both. To clearly illustrate thisinterchangeability of hardware and software, various illustrativecomponents, blocks, modules, circuits, and steps have been describedabove generally in terms of their functionality. Whether suchfunctionality is implemented as hardware or software depends upon theparticular application and design constraints imposed on the overallsystem. The described functionality may be implemented in varying waysfor each particular application, but such implementation decisionsshould not be interpreted as causing a departure from the scope of theimplementations.

The various illustrative blocks, modules, and circuits described inconnection with the implementations disclosed herein may be implementedor performed with a general purpose processor, a Digital SignalProcessor (DSP), an Application Specific Integrated Circuit (ASIC), aField Programmable Gate Array (FPGA) or other programmable logic device,discrete gate or transistor logic, discrete hardware components, or anycombination thereof designed to perform the functions described herein.A processor may be a microprocessor, but in the alternative, theprocessor may be any conventional processor, controller,microcontroller, or state machine. A processor may also be implementedas a combination of computing devices, e.g., a combination of a DSP anda microprocessor, a plurality of microprocessors, one or moremicroprocessors in conjunction with a DSP core, or any other suchconfiguration.

The steps of a method or algorithm and functions described in connectionwith the implementations disclosed herein may be embodied directly inhardware, in a software module executed by a processor, or in acombination of the two. If implemented in software, the functions may bestored on or transmitted as one or more instructions or code on atangible, non-transitory, computer-readable medium. A software modulemay reside in Random Access Memory (RAM), flash memory, Read Only Memory(ROM), Electrically Programmable ROM (EPROM), Electrically ErasableProgrammable ROM (EEPROM), registers, hard disk, a removable disk, a CDROM, or any other form of storage medium known in the art. A storagemedium is coupled to the processor such that the processor can readinformation from, and write information to, the storage medium. In thealternative, the storage medium may be integral to the processor. Diskand disc, as used herein, includes compact disc (CD), laser disc,optical disc, digital versatile disc (DVD), floppy disk and Blu-ray discwhere disks usually reproduce data magnetically, while discs reproducedata optically with lasers. Combinations of the above should also beincluded within the scope of computer readable media. The processor andthe storage medium may reside in an ASIC.

For purposes of summarizing the disclosure, certain aspects, advantagesand novel features have been described herein. It is to be understoodthat not necessarily all such advantages may be achieved in accordancewith any particular implementation. Thus, one or more implementationsachieves or optimizes one advantage or group of advantages as taughtherein without necessarily achieving other advantages as may be taughtor suggested herein.

Various modifications of the above described implementations will bereadily apparent, and the generic principles defined herein may beapplied to other implementations without departing from the spirit orscope of the application. Thus, the present application is not intendedto be limited to the implementations shown herein but is to be accordedthe widest scope consistent with the principles and novel featuresdisclosed herein.

What is claimed is:
 1. An apparatus for determining a relative positionof a wireless power transmitter from a wireless power receiver,comprising: a plurality of sense coils, each configured to generate arespective signal under influence of an alternating magnetic fieldcomprising a plurality of beacon signals occurring simultaneously, eachbeacon signal modulated with a unique spreading code; and a processorconfigured to determine the relative position of the wireless powertransmitter from the wireless power receiver based on the respectivesignal from each of the plurality of sense coils, wherein the respectivesignal generated by each of the plurality of sense coils comprises atleast: a first portion caused by a first beacon signal of the pluralityof beacon signals, a second portion caused by a second beacon signal ofthe plurality of beacon signals, and a third portion caused by a thirdbeacon signal of the plurality of beacon signals, wherein the processoris configured to estimate a relative phase angle of the first portion,and wherein the processor is configured to establish relative phasesynchronization in the time domain between the first portion, the secondportion, and the third portion by shifting a detection time instant byan amount that is a function of the relative phase angle between thefirst portion and the second portion.
 2. An apparatus for determining arelative position of a wireless power transmitter from a wireless powerreceiver, comprising: a plurality of sense coils, each configured togenerate a respective signal under influence of an alternating magneticfield comprising a plurality of beacon signals occurring simultaneously,each beacon signal modulated with a unique spreading code; and aprocessor configured to determine the relative position of the wirelesspower transmitter from the wireless power receiver based on therespective signal from each of the plurality of sense coils, wherein therespective signal generated by each of the plurality of sense coilscomprises at least: a first portion caused by a first beacon signal ofthe plurality of beacon signals, a second portion caused by a secondbeacon signal of the plurality of beacon signals, and a third portioncaused by a third beacon signal of the plurality of beacon signals,wherein the processor is configured to estimate a relative phase angleof the first portion, and wherein the processor is further configured toestablish relative phase synchronization in the frequency domain betweenthe first portion, the second portion, and the third portion by shiftinga phase angle of each of the first portion, the second portion and thethird portion by the relative phase angle.
 3. A method for determining arelative position of a wireless power transmitter from a wireless powerreceiver, comprising: generating, by each of a plurality of sense coils,a respective signal under influence of an alternating magnetic fieldcomprising a plurality of beacon signals occurring simultaneously, eachbeacon signal modulated with a unique spreading code; determining therelative position of the wireless power transmitter from the wirelesspower receiver based on the respective signal from each of the pluralityof sense coils, wherein the respective signal generated by each of theplurality of sense coils comprises at least: a first portion caused by afirst beacon signal of the plurality of beacon signals, a second portioncaused by a second beacon signal of the plurality of beacon signals, anda third portion caused by a third beacon signal of the plurality ofbeacon signals; estimating a relative phase angle of the first portion;and establishing relative phase synchronization in the time domainbetween the first portion, the second portion, and the third portion byshifting a detection time instant by an amount that is a function of therelative phase angle between the first portion and the second portion.4. A method for determining a relative position of a wireless powertransmitter from a wireless power receiver, comprising: generating, byeach of a plurality of sense coils, a respective signal under influenceof an alternating magnetic field comprising a plurality of beaconsignals occurring simultaneously, each beacon signal modulated with aunique spreading code; determining the relative position of the wirelesspower transmitter from the wireless power receiver based on therespective signal from each of the plurality of sense coils, wherein therespective signal generated by each of the plurality of sense coilscomprises at least: a first portion caused by a first beacon signal ofthe plurality of beacon signals, a second portion caused by a secondbeacon signal of the plurality of beacon signals, and a third portioncaused by a third beacon signal of the plurality of beacon signals;estimating a relative phase angle of the first portion; and establishingrelative phase synchronization in the frequency domain between the firstportion, the second portion, and the third portion by shifting a phaseangle of each of the first portion, the second portion and the thirdportion by the relative phase angle.